lekhnathgaire7
Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

find the limiting value using L hospital​

Find The Limiting Value Using L Hospital class=

Sagot :

sqdancefan

Answer:

  -1

Step-by-step explanation:

The expression evaluates to the indeterminate form -∞/∞, so L'Hopital's rule is appropriately applied. We assume this is the common log.

  d(log(x))/dx = 1/(x·ln(10))

  d(log(cot(x)))/dx = 1/(cot(x)·ln(10)·(-csc²(x)) = -1/(sin(x)·cos(x)·ln(10))

Then the ratio of these derivatives is ...

  lim = -sin(x)cos(x)·ln(10)/(x·ln(10)) = -sin(x)cos(x)/x

__

At x=0, this has the indeterminate form 0/0, so L'Hopital's rule can be applied again.

  d(-sin(x)cos(x))/dx = -cos(2x)

  dx/dx = 1

so the limit is ...

  lim = -cos(2x)/1

  lim = -1 when evaluated at x=0.

_____

I find it useful to use a graphing calculator to give an estimate of the limit of an indeterminate form.

View image sqdancefan
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.