Question

Calculus Differentiation???

Answer 1

Use the definition of the derivative to determine if the function is differentiable at x = 0.\[f \prime(x)=\lim_{h \rightarrow 0} \frac{ f(x+h)-f(x) }{ h }\] if \[f(x)=\ln(x)\]

Answer 2

A. f(x) is differentiable at x=0
B. f(x)is not differentiable at x=0 because the \[\lim_{h \rightarrow 0}\frac{ f(x+h) - f(x) }{ h }\] does not exist at x=0
C. f(x) is not differentiable at x=0 because the \[\lim_{h \rightarrow 0}\frac{ f(x+h) - f(x) }{ h }\] increases without bound.
D. f(x) is nor differentiable because the \[\lim_{h \rightarrow 0}\frac{ f(x+h)-f(x) }{ h } = \infty\] at x=0

Answer 3

Did you do the work? This is simply tedious algebra work.

Answer 4

i think its b

Answer 5

i got a bit confused. I can try it again though.

Answer 6

i got that it doesn't exist at x=0?

Answer 7

@abb0t

Answer 8

it was correct :)