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Hi there, I'm currently stuck on a maths question. Find the limit as x approaches 0 for (1+sinx)^cotx I've put logs on both sides and am attempting to use hopitals rule but don't know where to proceed from here.

The slope of a curve Y = f(x) is given by dy/dx=(X-1)(x-2)^2(x-3)^3(x-4)^4(x-5)^5. (a) For what value or values of x does y have a local maximum/minimum? Justify your answer. I know the maximum/min occurs when dy/dx = 0, which in this case is 1,2,3,4,5 bu...

Let f be a function such that f(−6)=−6, f(6)=6, f is differentiable for all real values of x and −1≤f'x≤1 for all real values of x. Prove that f(x)=x for all −6≤x≤6 I tried applying the mean value theorem here but I'm not sure where to start.

Read this quote by henry david Thorea from Walden. "We must learn to reawaken and keep ourselves awake, not by mechanical aids, but by an infinite expectation of the dawn, which does not forsake us even in our soundest sleep. I know of no more encouraging...

AHHH ok ok thank you so much!!

Ur answers are all WRONG i just got A 0 thxxxxx

A and c