1
vote
1answer
33 views

Finding the zeros of trionometric polynomails.

I have a question about something I've struggled with for a while: Finding the zeros of trigonmetric polynomials. Let me show you a problem I am solving and you guys can tell me if I got the right ...
0
votes
1answer
57 views

solving the equation

let there be a function $ f(x)= \ln x-kx^2, k>0$ determine for whihc values of $ k$ ,the equation $f(x)=0.5$ has a single solution; attemp to solve: $$0.5 = \ln x-kx^2$$ $$kx^2 +0.5 = \ln x $$ ...
1
vote
4answers
82 views

Antiderivative of $\frac{1}{1+\sin {x} +\cos {x}}$

How do we arrive at the following integral $$\displaystyle\int\dfrac{dx}{1+\sin {x}+\cos {x}}=\log {\left(\sin {\frac{x}{2}}+\cos {\frac{x}{2}}\right)}-\log {\left(\cos {\frac{x}{2}}\right)}+C\ ?$$
2
votes
2answers
121 views

Solve for $x$: $\frac1e = e^{2x}$

I tried making it to $e^{-1} = e^{2x}$ and had the exponents equal each other $-1=2x$ and the I solved for $x$, making it $x=-1/2$, but that answer is wrong. please help I don't know why that ...
2
votes
2answers
87 views

Evaluation of $\int\frac{\sqrt{\cos 2x}}{\sin x}dx$

Evaluation of $$\displaystyle \int\frac{\sqrt{\cos 2x}}{\sin x}dx$$ $\bf{My\; Try::}$ Let $\displaystyle I = \int\frac{\sqrt{\cos 2x}}{\sin x}dx = \int\frac{\cos 2x}{\sin^2 x\sqrt{\cos 2x}}\sin xdx ...
0
votes
3answers
61 views

How to solve for $x$ for $\frac{1}2 x^{-1/2}- \frac14x^{-3/4}$

This is a derivative and I am trying to find the max and min. Right now I am trying to solve for x. $$\frac{1}2 x^{-1/2}- \frac14x^{-3/4}$$ $$\frac{1}{2 x^{1/2}}- \frac1{4x^{3/4}}$$ $$\frac{1}{2 ...
2
votes
4answers
59 views

Determined or not?

the function $\dfrac {2x}{3x-\sqrt{x} }$ is not derterined for values of $x$ equale or samller than zero, though when I take the limit $ \lim_{x \to 0^+} \dfrac {2x}{3x-\sqrt{x} }$ the output is zero ...
0
votes
1answer
60 views

what is the coefficient of following expression

what is the co-efficient of $x^{50}$ in the expansion of $$\frac{1}{(1-x^{1.7})(1-x^{1.8})(1-x^{2.6})(1-x^{3.0})(1-x^{4.0})(1-x^{6.7})(1-x^{7.5})(1-x^{8.2})}$$ can you please explain me the logic
2
votes
2answers
101 views

Derivative of $(-2)^{x+1}$ [on hold]

Can we compute the derivative of $(-2)^{x+1}$? This may sound silly, but think about it. We cannot apply any of our formulae on it. I think we may have to go old school with this one
0
votes
1answer
29 views

Double checking my progress on finding critical numbers

still cramming for the test tomorrow. (This cram has lasted most of my weekend) I'm having trouble with determining the critical values for this example problem. The problem is as follows: $$F(x) = ...
2
votes
2answers
77 views

Pick a smart function

Our teacher wants us to find a function $f$ on $(0,\pi)$ such that $$\sqrt{\sin(x)} f(x)^{\frac{1}{4}} =k_1 + \cos(x)$$ and $$\sqrt{\sin(x)} f(x)^{-\frac{1}{4}} = k_2 + \cos(x).$$ The two constants ...
0
votes
3answers
54 views

Showing $\lim_{n \to \infty}\left(1 + \frac{x}{n}\right)^n = e^x$ using implicit and log differentiation

Hey guys I'm looking over my review sheet for an upcoming test and I'm having trouble with this problem. Apparently I'm supposed to use implicit differentiation and log differentiation, and I'm ...
4
votes
1answer
106 views

find the minimum value of $x^2-6x+9+ \dfrac{64}{x^2}$

Looking for an elegant solution. I can do by brute force, that is finding derivative and double derivative. All Ideas will be appreciated and tried by me.
0
votes
1answer
38 views

How to rewrite this radicand as a perfect square.

I'm not sure how to rewrite $$\sqrt{162+81e^{18t}+81e^{-18t}}$$ in the form $\sqrt{\text{something}^2}$. It says to keep in mind that $e^{z} \cdot e^{-z}=1$. Thank you.
3
votes
5answers
192 views

Calculating the area

For the two graphs $ \frac{x^3+2x^2-8x+6}{x+4} $ and $ \frac{x^3+x^2-10x+9}{x+4} $, calculate the area which is confined by them; Attempt to solve: Limits of the integral are $1$ and $-3$, so I took ...
0
votes
2answers
51 views

Find the Intervals when $\cos\left(\frac{1}{2}\pi x^2\right)$ is positive.

I am looking for a general solution, not in any restricted domain.
0
votes
1answer
24 views

Calculating optimum values of $u$ and $m$ from $\mathbb V(\bar {y_2}\prime)=\frac{S_2^2(n-u\rho^2)}{n^2-u^2\rho^2}$

I have to find optimum sample size in sampling on two occasions. Suppose that the samples are of the same size n on both occasions. In selecting the second sample, $m$ of the units in the first ...
3
votes
2answers
42 views

Composition of functions is constant in $\mathbb{R^2}$.

Let $\hspace{0.05cm}f:\mathbb{R^2}\to\mathbb{R^2}$ $\hspace{0.05cm}$ and $\hspace{0.05cm}$$g:\mathbb{R^2}\to\mathbb{R^2}$ $\hspace{0.05cm}$ be such that$\hspace{0.05cm}$ $g\circ f$$\hspace{0.05cm}$ ...
0
votes
3answers
43 views

Trouble with Logarithmic Differentiation

Hey guys I'm trying to find the derivative of this equation using logarithmic differentiation but I'm having some trouble. Wolfram Alpha is giving me different answers and I'm having difficulty ...
3
votes
2answers
50 views

The right procedure on difficult related rates problems

I'm pretty sure the sample problems my teacher gives to us violate some article of the Geneva convention. I'm in talks with my embassy about that, but in the mean time maybe you guys could look over ...
1
vote
3answers
30 views

Related Rates Ladder Problem with Angles

The problem is as follows: A 13-foot ladder leans against the side of a building, forming an angle θ with the ground. Given that the foot of the ladder is being pulled away from the building at the ...
2
votes
0answers
21 views

Rendering the derivative of composite functions from a graph

I'm on a workbook problem and I want to make sure I'm doing it properly. The problem asks me to find the derivatives of composite functions when given only the graphs of the original functions, here ...
1
vote
1answer
53 views

Simplifying equation variables

I have two emissions equations I am working with that are giving me problems. The first problem I was able to solve my self, the second I have not and am not sure if it is possible. Emission ...
1
vote
3answers
54 views

surjective, but not injective linear transformation

$T$ is a transformation from the set of polynomials on $t$ to the set of polynomials on $t$. So, the input to $T$ should be a polynomial, and the output should be some other polynomial. Two common ...
2
votes
3answers
63 views

Using the Chain Rule to prove trig derivatives

I'm having trouble with this problem, I'm not sure how to tackle it and I was wondering if somebody could set me on the right path. The problem is as follows: Use the Chain Rule to show that if ...
0
votes
3answers
71 views

Possibly not complete answer when integrating using substitution

$$\int e^{\sqrt{x}} \,dx $$ Making substitution $ u= e^{\sqrt{x}} $ $ \ln(u) = \sqrt{x} $ (do no know how to call that (taking logarithm of both sides..?)) $ x = \ln^2(u) $ Derivating both sides $ ...
1
vote
1answer
32 views

Solve this with CBS

How can you see the mínimum value of $ 1/x + 4/y + 9/z $ with x+y+z=1 using the CBS inquality? I have seen a proof of that that use trigonometric substitutions, but i don´t see as one-step the ...
1
vote
1answer
72 views

How to solve this graphing question?

$ \frac{|x-2|} {(x^2-4)}+\frac{(x-2)} {|x-2|} = b $ determine for which values of $b$ the equation has one and only solution. I tried sketching the graph, but was unable to do so accuratly...also, ...
0
votes
3answers
60 views

Trouble finding the derivative of an expression

I could use your help. I've spent over 20 minutes on this problem and my inability to solve it has my questioning my calculus skills. If someone could show me where I messed up and walk me through the ...
1
vote
2answers
32 views

Proving double derivatives with the chain rule (I think?)

Hey StackExchange I'm having trouble understating where to start with this problem, I'm supposed to prove something about double derivatives and the chain rule but I'm having trouble understanding ...
0
votes
1answer
17 views

Discovering the derivatives of functions combined with trig values.

Hey StackExchange I have a problem that I don't really understand and I could use some hints for starting it. Suppose $m(\frac{\pi}{3}) = 4$ and $ m'(\frac{\pi}{3}) = -2$, and let $g(x) = m(x)\sin x$ ...
0
votes
2answers
36 views

solving $|(x-3)(x-1)| $$\le$ $|\frac{1-x}{x-3}|$ graphicly [closed]

how to solve $|(x-3)(x-1)| $$\le$ $|\frac{1-x}{x-3}| $ in the graphic method?
1
vote
1answer
35 views

Formula alteration

is there any way to transform the formula$ \frac {1-x}{x-3}$ into something that can be easily sketched, or which will help eliminate $x$ from the denominator?
2
votes
1answer
39 views

Greatest value of f

If $f'(x)=6-x$ then which of the following has the greatest value? $f(2.01)-f(2)$ $f(3.01)-f(3)$ $f(4.01)-f(4)$ $f(5.01)-f(5)$ $f(6.01)-f(6)$ I know the answer is $f(2.01)-f(2)$ but how to prove?
0
votes
0answers
19 views

Prove (non)differentiability in piecewise functions

I'm looking for some help on proving that this function is not differentiable at a specific value. My first instinct is to approach the limit of the value from positive and negative, but that doesn't ...
1
vote
3answers
31 views

Factoring when differentiating expressions

I'm having trouble with differentiating a expression. I do it one way, wolfram alpha does it another. Let me show you what I mean. The original expression is this: $$\frac{1}{2u^3}$$ I start by ...
1
vote
1answer
32 views

consider a square of side length $x$, find the area of the region which contains the points which are closer to its centre than the sides.

Any ideas how to start. I am having trouble figuring out the region itself All ideas are appreciated thanks
7
votes
1answer
75 views

Find the maximum value of $ \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4-x^2+1} $

If $x\in\mathbb{R}$ find the maximum value of $$ \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4-x^2+1} $$ I tried this: Let $$y= \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4-x^2+1}$$ For maxima ...
0
votes
1answer
13 views

Drawing a graph based on derivative properties

I'm just doing some math and I could use some help. The problem asks me to draw a graph based on the following properties: $f'(x) > 0$ if $\lvert x\rvert < 2$ $f'(x) < 0$ if $\lvert x\rvert ...
2
votes
1answer
36 views

Using the definition of a derivative

I'm here with a maths problem. I'm trying to find the derivative of an expression but when I calculate it I get different answers depending on if I use the power rule or definition of a derivative. ...
3
votes
4answers
237 views

inequality method of solution

Im looking for an efficent method of solving the following inequality: $$\left(\frac{x-3}{x+1}\right)^2-7 \left|\frac{x-3}{x+1}\right|+ 10 <0$$ I've tried first determining when the absolute value ...
3
votes
3answers
42 views

Finding domain of $f\text{ o }g$

I am having a small question, please don't close this before answering, I just want to know whether its a matter of convention or not. If $f(x) = \dfrac{1}{x}$ and $g(x) = \dfrac{1}{x}$ $ $ Then ...
0
votes
0answers
41 views

solving the logaritham [duplicate]

I was trying to solve: $\log_2 x \cdot \log_{0.25} x \cdot \log_{0.125} x \cdot \log_{16} x > \frac {2}3$ heres my attempt at it; using logaritham laws and a little algebra we get from $\log_2 x ...
1
vote
3answers
70 views

Trouble finding the derivative of $\frac{4}{\sqrt{1-x}}$

I've been trying to figure out how to differentiate this expression, apparently I don't know my differentiation rules as much as I thought. I've been trying to use Wolfram Alpha as a guide but I'm at ...
0
votes
4answers
54 views

Alternatives to quotient rule

Hey StackExchange I have a question for you guys. I have a homework problem and my first intuition is to use the quotient rule (or re-write the expression to use the product rule) but the ...
0
votes
2answers
66 views

Mathematical Induction Problem with Fraction

$$(3n-2)^2=\frac{n(6n^2-3n-1)}{2}$$ I can't seem to solve it out to the point where I can prove it right or wrong. I always hit some sort of roadblock where I don't have enough info to prove it ...
1
vote
2answers
32 views

What will be the range of $f(x)= \frac{12}{\sqrt{(15-2x-x^2)}}$

Here's my try: Since the denominator involves a square root so I solved the following inequality: $15-2x-x^2>0$ which gives a solution set of $x=(-5,3)$. This is the domain of $f(x)$. However since ...
0
votes
3answers
26 views

Map (-1500, 1500) on scale of (0, 100).

I've a minimum value = -1500 & maximum value 1500. Now, I've a scale of 0 to 100. How can I map my min & max value to this scale. That is, if I select 99 on scale, it should return 99% of ...
1
vote
3answers
380 views

The high power integral

Im trying to solve the indefinite integral $$\int\frac{x}{(x^2+4)^3} \, \mathrm{d}x $$ I tried applying polynimial division and breaking to partial fractions but it didnt help...are there any other ...
5
votes
3answers
119 views

Finding a formula for specific limits

Hey guys I have a math problem I'm not sure how to go about solving. If someone could give me a systematic method for solving these kinds of problems that would be great. The problem is as follows: ...