1
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2answers
31 views

Using linear approximation to approximate $\sqrt{81.3}$

Use linear approximaiton to approximate $\sqrt{81.3}$ as follows: Let $f(x)=\sqrt{x}$. The equation of the tangent line to $f(x)$ at $x=81$ can be written in the form $y=mx+b$ where $m$ is:____ and ...
0
votes
1answer
18 views

Finding linear approximation at $x=0$ to $\frac{1}{\sqrt{2-x}}$

The linear approximation at $x=0$ to $\dfrac{1}{\sqrt{2-x}}$ is $A+Bx$, where $A$ is: _____, and where $B$ is: ______. I don't understand what this question is asking and how to solve it. I ...
1
vote
1answer
32 views

Estimate value using Lagrange's MVT

Estimate the value of $51^{1/2}$ using Lagrange's MVT. Answer both in terms of inequalities and approximately estimated value. My method: Let $f(x)=x^{1/2}$ defined in $[49,51]$ and ...
0
votes
3answers
38 views

For what values of $r$, $x^r$ has infinite slope at $x=0$?

I'm learning calculus form MIT OCW 18.01SC. In session 23 (it's about linear approximation), prof computes linear approximation near $0$ of some basic functions. $$\sin{x}, \cos{x}, e^x, \ln{(1+x)}, ...
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3answers
63 views

Where did the linear approximation/linearization formula come from?

Where did the linear approximation/linearization formula come from? I understand that it takes root in the point-slope form and slope intercept form of a linear equation, but I don't understand where ...
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1answer
92 views

Which number is larger if f'(x) is a differentiable increasing function for all x?

Suppose is a differentiable increasing function for all x. Which number is the larger and why? or ? I believe f(x) must be concave up everywhere since the derivative is increasing, but I am not ...