Recent content by macjack

Can anyone tell me whether sin|x| and cos|x| is differentiable at x=0 ? As far as i know, cos(x) and sin(x) is differentiable at all x. If i try to solve this, lim h->0 (f(x+h) - f(x))/h when x=0, and substitute cos|x| for f(x). lim h->0 (cos|h| - cos|0|)/(h) = 1, so cos|x| is...

what about the third statement ? >3) if the order of the denominator is lesser than the top, then the limit is >infinity or no limit (i have a doubt here)...am i correct with this condition.. Did anyone know what is the correct answer for this ??

why i said it is 0 is ? there is a common trick when you take lim x->infinity, based on the powers of the numerator and denominator in a polynomial equation. 1) if the orders are same , then just take the coefficients of higher order terms and divide it. 2) if the order of denominator is...

thanks ice109 thanks ... i am a newbie into calculus..didnt face the limits of sequences till now. anyway thanks for your help.

Thanks Thanks for your response. The answers given are a) The sequence approaches the limit from RHS b) The sequence approaches the limit from LHS c) The sequence oscillates about the limit d) none of the above. None of my answers and few of them answers also didnt match this...

can you please help me to find the limit ? limit n->infinity ((-1)^(n-1))/n ? i tried to find the limit using the limit at infinity trick,...i got the value as 0 but the solution given are not matched. can you please help me out ? Thanks Mc

I am trying to solve the exercise in this link, please let me know if i am doing something wrong. ( i didn't find answers to this exercise that's why i am sending it here) http://www.libraryofmath.com/limits-with-piecewise-functions.html exercise 1 ---------- a) lim x->3- f(x) = 7 b)...

am i correct ? f(x) = 1- (x-1)^(2/3) so f'(x) = 0 - (2/3) (x-1)^(-1/3) = (-2/3) / ((x-1)^(1/3)) so if x=1, bottom x-1 will become 0 and result becomes infinity. if x<1, then you will get a positive value and if you x>1 you will get a negative value ! So this function is...

thanks Office_Shredder, thanks for the explanation. Yes i found out the limits (both left and right)for my latest problem |x| in range [-1,1]. It's not same. Now let me come to the problem, you found that |x| is not differentiable at x=0.How did you find that ? (We have seen this example in...

Thanks for the reply. For the above two equations i could able to prove that it is not satisfying rolle's theorem.For the first one f(a) Not equal to f(b) and for the second one f'(x) is infinity. BTW.. if i change the range from [1,2] to [-1,1](for the first f), f(a)= f(b) then do i have to...

Homework Statement check whether the rolle's theorem is valid f(x)= x^2 in [1,2] f(x)= 1-(x-1)^(2/3) in [0,2] my question is, how do you usually find whether these equations are differentiable/continuous ?? For some equation, we used to plot the graph and find any corner points are...