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3answers
35 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
54 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
73 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 ...