For basic questions about limits, derivatives, integrals, and applications, mainly of one-variable functions.

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0answers
11 views

how to add shipping cost to unit cost

If I have x number of units at DIFFERENT unit cost from supplier, after shippings costs, how much shipping expenses will each unit carry? Basically I want to know how much each unit will jump after ...
0
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1answer
16 views

Query regarding an alegbraic inequality

Do we have any inequality of the type $(a-b)^q \geq C_q(a^q-b^q),$ where $q>0$ and $a,b$ are real numbers?
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3answers
30 views

Calculus (integration [multiplication])

Determine $\int e^{2x} \sqrt{e^x+1}dx$ Is there a multiplication rule for integration or something?
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3answers
31 views

Calculus (what is y when x is?)

Given $y>0$ and $$dy/dx = (3x^2+4x)/y$$ If the point $(1,rad10)$ is on the graph relating x and y, then what is $y$ when $x=0$? I'm not sure whether or not to integrate, or just plug in the ...
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1answer
39 views

sum of infinite series 1/2 + 1/4 + 1/8 + … [on hold]

goto 324 here: Visually stunning math concepts which are easy to explain Someone comment this writing the claim as such: Another way to think of this is that 1/2 + 1/4 + 1/8 = 0.111...binary = ...
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1answer
40 views

How to find the limit $\lim_{x\to 0} ( 4x/\sin 2x + x\cos2x )$?

Compute $$\lim_{x\to0}\left[-\dfrac{4x}{\sin 2x} + \dfrac{x}{\cos 2x}\right]$$ Obviously I can't plug in 0. I noticed the sin and cos are both 2x. Is there a way to combine them into tan? I don't ...
-1
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4answers
38 views

Calculus (limits)

Compute $$\lim_{t\to0}\frac{\tan\left(\dfrac {1}4\pi + t\right) - \tan\left(\dfrac{1}4\pi\right)}t$$ Alright, so I'm taking the derivative first. Is there an easier way to take the derivative of ...
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0answers
18 views

area and limit of the shaded region

Consider the shaded region outside the sector of a circle of radius 12 meters and inside a right triangle. a) write the area A= f(θ) of the region as a function of θ. I found the area of the ...
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1answer
28 views

Complex roots (review) (advise)

I have to find the complex roots and want a review of my procedure to see if is correct A. $$\sqrt{3i}$$ $$\left |z \right |=3 $$ $$phase= 90^{\circ}=\displaystyle\frac{\pi}{2}$$ ...
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2answers
47 views

Simple Derivative paradox

Suppose I define $y(x)=x^3$ $${dy(x) \over dx} = 3x^2$$ $${dy(x) \over dy} = 1 = 3x^2 \frac{dx}{dy} = 0\text{ since }x \neq f(y)$$ $1 \neq 0$ If you take the differential $d()$ where $dy(x)$ then ...
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1answer
50 views

Calculus (advanced integration)

Compute $\int (5^x+2e^{5 \ln x})dx$ The $5\ln x$ part confuses me. So far I have $5^x/\ln 5\:\:$
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0answers
10 views

Domain of function for a sector

I seem to have forgotten how to find the domain of a sector.The question asks to find the domain of the function 72(tan $\theta$ - $\theta$). This question was based on a previous question asking to ...
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1answer
41 views

Evaluate the limit, if it exists

In Exercises 5-34, evaluate the limit, if it exists. If not, determine whether the one side limit exists (finite or infinite). 26. $$\lim_{x\to ...
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0answers
82 views

Problem with trigonometric substitution proof

I'm sad, I can't get it. I know perfectly how to integrate using the mechanical process described in the books, but I want to understand the proof of it. My book (Stewart) says: In general we can ...
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3answers
15 views

Disk Method Problem, where Axis of Rotation is Shifted from the Y-Axis

Could somebody please check my work here? The textbook answer is 224pi/15, but I'm getting something different. Is it a set up error? Question: Find the volume of the solid generated by revolving ...
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2answers
44 views

Calculus (value of $c$)

The slope of the tangent line to the graph of $4x^2+cx-2e^y=-2$ at $x=0$ is $4$. Give the value of $c$. What I'm confused about here is the 3 variables. Is it implicit differentiation or something? ...
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2answers
22 views

How to find the slope of a secant line of the graph of a function?

The point $P(5,-2)$ lies on the curve $y=\large\frac{2}{4-x}$. (a). If $Q$ is the point $(X,\large\frac{2}{4-x})$, find the slope $M_{pq}$ of the secant line $PQ$ (correct to six decimal places). ...
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2answers
24 views

How to find local maximum of the function $f(x) = x^3-9x^2+24x+4$?

Give the value of x where the function $f(x) = x^3-9x^2+24x+4$ has a local maximum. a) -4 b) 4 c) 2 d) 3 e) -2 I graphed it and I'm not sure how to find the local max
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0answers
15 views

<html5> draw circle by arc and triangle [on hold]

I want if click the retacgle, draw a triangle around the circle. source code like this... but, triangle was not good each of positions.. How can i draw a triangle around the circle like attached ...
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2answers
25 views

Find the equation of normal line to the graph of given function

Give the equation of the normal line to the graph of $$y = 2x \sqrt{x^2+8} + 2$$ at the point $(0,2)$ What I've done so far is: Taken the derivative and got $$(2x^2)/\sqrt{ x^2+8} + ...
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1answer
24 views

Finding eq of tan to the curve

I am trying to figure out how to find the eq to the tan to the curve x = cost + cos2t, y = sint + sin2t, (-1,1) I'm lost at the point where you plug in t in order to find the slope. I have the ...
5
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3answers
184 views

Calculus (Integration)

Is there a simple way to integrate $\displaystyle\int\limits_{0}^{1/2}\dfrac{4}{1+4t^2}\,dt$ I have no idea how to go about doing this. The fraction in the denominator is what's confusing me. I tried ...
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2answers
32 views

Integration by parts

Integrate using integration by parts: $F(y) = (y+1)e^{-y}$ Find: Evaluate the $\int_{a=0}^{b=\infty}F(y)\;dy$ using integration by parts. Thus far, I've distributed the $e^y$ term and split ...
3
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1answer
31 views

Studying the function $f(x) = x^4-6x^2$ using derivatives: minima, maxima, inflection, concavity

(I know this is my second question today, but I'm explaining what I'm doing so I hope it's okay) Consider the graph of $f(x) = x^4-6x^2$. a) Find the relative maxima and minima (both x and y ...
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0answers
19 views

Math issue implementing an invoice API [on hold]

Okay, so, I have $2$ separate systems: An invoice record database on an external site, I do not have access to the code here. An prestashop e-commerce installation, where i am developing a plugin. ...
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0answers
19 views

sketch the region in the xy-plane

Sketch the region in the xy-plane defined by the equation or inequalities $|x|<7$ and $|y|<4$ Im not quite sure how I am supposed to do this.
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1answer
36 views

When does a particle with given acceleration change the direction of motion?

A particle moves along the x-axis so that its acceleration at any time $t\geq0$ is given by $a(t)=12t-4$. At time $t=1$, the velocity of the particle is $v(1)=7$ and its position is $x(1)=4$. ...
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1answer
7 views

Angles of which locations of points corresponding to distances intersect each other

Original problem : In the $XY$ plane,Let $P_1$ and $P_2$ two points with coordinates $(-1,0)$ and $(1,0)$. $C_1$ is the locus of points whose sum of distances to $P_1$ and $P_2$ is $4$. $C_2$ is the ...
0
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1answer
29 views

Taylor series of Lambert W function $W_{-1}(x)$

Is possibile to find the closed form for the Taylor series of Lambert W function $W_{-1}(x)$? What do you think? On Wikipedia there is the Taylor series of $ W_0$ around $0$.
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5answers
55 views

Derivative of $\ln(1+\sin 2x)$

Differentiate the equation $y=\ln(1+\sin2x)$. It will be something to do with the $\frac{d}{dx}\{\ln\:x\}=\frac{1}{x}$ rule, but I'm not sure how to deal with the $\sin2x$ term.
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2answers
79 views

$\sum \tan ( 1/n)$ diverges

Show that the series $$\sum_n \tan\left(\frac{1}{n}\right)$$ diverges. I dont have any attempt to do, since I am having some troubles with series including geometric functions. I would be glad if I ...
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1answer
47 views

Show that $f^{[n]}(0)=0$ for all $n=0,1,2…$

Let $$f(x)=\left\{ {\matrix{ {{e^{ - {1 \over {{x^2}}}}},x \ne 0} \cr {0,x = 0} \cr } } \right.$$ Show that $f^{[n]}(0)=0$ for all $n=0,1,2,\cdots$ The proof: First note that for ...
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1answer
30 views

Generalized Logarithmic Integral - reference request

This page at I&S forum defines the Generalized Logarithmic Integral as $$L\left[ \begin{matrix} a,b,c \\ d,e,f \end{matrix};z\right] =\int_0^z \frac{\log^a x \log^b(1-x)\log^c(1+x)}{x^d (1-x)^e ...
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4answers
54 views

perpendicular bisector of AB

Let $A(-6,9)$ and $B(10,-3)$ be points in the plane Find an equation of the perpendicular bisector of $AB$ the answer I get is $y=(4/3)x+(1/3)$ but it is not correct.
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1answer
20 views

Derivatives on both side of an asymptotic equivalence

Suppose I have two continuous function $x(t)$ and $w(t)$. If I have that $x(t)\rightarrow w(t)$, does that imply that $\dot{x}(t) \rightarrow \dot{w}(t)$?
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1answer
34 views

Finding the point on a curve that has a tangent slope of 7

I am asked to find the point on a curve $y=x^2-3x$ that has a slope of the tangent $7$. So I started first with finding the derivative: \begin{align*} f'(x) &=\lim_{h \to 0} ...
2
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1answer
26 views

Convergence study of a series of functions

I am studying the convergence of the series $$ \sum_{n=0}^{\infty}\frac{\sin (x^n)}{(1+x)^n} $$ where $x \in \mathbb R$. My initial approach was to use the ratio test, but I am not getting to ...
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1answer
52 views

Derive the formula for the sum of the first $n$ squares using derivatives and integrals

I wanted to prove the formula for sum of squares without using induction and thought using derivatives would be the easiest approach ...
3
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1answer
53 views

Nonsensical result in the midst of calculating an integral via substitution.

I was just calculating an integral via a trigonometric substitution and ended up with $\color{red}{ \text{something pretty nonsensical} }$ but $\color{blue}{ \text{reversing the substitution} }$ ...
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3answers
38 views

How to shift $y=-\ln(-x)$ so that the $x$ intercept is $0$ instead of $-1$?

I would like this function shifted to the right. I'm not quite sure how. As positive values of $x$ grow, I need increasing slope.
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1answer
10 views

Check me- Speed(Arc Length) of Parametric Equations

A ferris wheel has height = 100 ft and completes 1 revolution in 3 minutes at a constant speed. Compute the speed of a rider in the ferris wheel. Ferris wheel = circle modeled by x= cos t ; y = sin t ...
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2answers
247 views

Is there such splitting?

Does there exist a set $A \subset [0,1]$ s. t. for every polynomial $P(x)$ of degree less than or equal to $4$ the relation between the Riemann integrals $$\int_A P(x)\,dx= \int_{[0,1]\setminus ...
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1answer
30 views

Evaluating $\ln(\cos x))$ using Taylor expansion

Evaluate $\ln(\cos x)$ at $x_0=0$ and with the order of $n=4$. Noticing that $\ln(\cos x) = \ln(1+ \cos x - 1)$ we can use $\ln(1+x)$ Taylor series. Now, I've read I should use: $$\ln(1+x) = x - ...
2
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1answer
41 views

Double Integral of a piecewise function

If $F(x,y)$ is defined as $F(x,y) = x+y$ when $0 < x + y < 1$ and $0$ elsewhere, then find $$\int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty} F(x, y) \,dx \,dy$$. Math note: I've ...
2
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1answer
28 views

Surjective function from a set of funtions to itself

Let a function be defined by $f \longmapsto f'$ acting from the set of all polynomials to itself. I am asked if this is surjective. I would like to think it isn't, but I'm in doubt how I should ...
3
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1answer
14 views

inflection point of cubic bezier with restrictions

Say you have this type of cubic Bézier curve: The 4 control points A,B,C,D have restrictions: A & B have the same Y-axis coordinate C & D have the same Y-axis coordinate B & C have ...
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2answers
53 views

Finding the integral of $(x^2+4x)/\sqrt{x^2+2x+2}$

Can somebody explain me how to calculate this integral? $$\int \frac{\left(x^2+4x\right)}{\sqrt{x^2+2x+2}}dx$$
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17 views

Show equations determine local functions and determine $\frac{du}{dx}$

Show that the pair of equations: $x^2-y^2-u^3+v^2+4=0$, and $2xy+y^2-2u^2+3v^4+8=0$ determine local functions $x(u,v)$ and $y(u,v)$ defined for $(u,v)$ near $u=2$ and $v=1$ such that $x(2,1)=2$ and ...
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1answer
43 views

Area of the region bounded by graphs of two exponentials.

Let S be the region in the first quadrant bounded by the graphs of $y = e^{-x^2}$ and $y = 2x^2$, and the y axis. a) Find the area of the region S. So when I integrate, is it from 0 to .5931? I ...
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1answer
44 views

$f\in C(\mathbb{R})$. What does it mean?

$f\in C(\mathbb{R})$. What does it mean? My guess is "Differentiable on $\mathbb{R}$" but I'm not sure.. Thanks.