Question

lim (1-x + lnx) / (1 + cos pix)
x->1

Answer 1

\[\lim_{x \rightarrow 1} \frac{-1 + \frac{1}{x}}{-\pi \sin \pi x} \]

Answer 2

that's 0/0 so i guess i need to use L'H rule again... but not sure how on that

Answer 3

derivative of top --> -1/x^2

derivative of bottom --> -pi^2 *cos(pix)

limit = -1/pi^2

Answer 4

could you explain how you got those derivatives... did you use quotient rule?

Answer 5

no, to use l'Hopital's rule, just take the derivative of the numerator and derivative of the denominator... do not do quotient rule.

Answer 6

i understand that, but in the numerator itself, is the quotient rule used? i guess i don't know how to take the derivative of -1 + 1/x

Answer 7

1/x = x^-1
use power rule
--> -x^-2 = -1/x^2

Answer 8

actually quotient rule would work as well but not really needed when top is a constant

Answer 9

ok got the numerator, still a bit confused on the denominator

Answer 10

chain rule
derivative of sin is cos, derivative of pi*x is pi

Answer 11

k, not sure how to simplify top and bottom now..

Answer 12

i'm looking at what you posted for numerator and denom. that's what i got, but how to go from there to -1/pi^2 ?

Answer 13

hah! you just plug in the 1 for x. got it!