Get the answer to "Find the following limit. limx→+∞(3−12x3x+5+csc⁡πx+π4x)"

snowlovelydayM

Answered question

2021-02-12

Find the following limit.

lim_{x \to + \infty} (\frac{3 - 12 x}{3 x + 5} + \csc \frac{π x + π}{4 x})

Neelam Wainwright

Skilled2021-02-13Added 102 answers

Given:

lim_{x \to + \infty} (\frac{3 - 12 x}{3 x + 5} + \csc \frac{π x + π}{4 x})

Solution:

lim_{x \to + \infty} (\frac{3 - 12 x}{3 x + 5} + \csc \frac{π x + π}{4 x}) = lim_{x \to + \infty} (\frac{3 - 12 x}{3 x + 5}) + lim_{x \to \infty} (\csc (\frac{π x + π}{4 x}))

= lim_{x \to + \infty} (\frac{x (\frac{3}{x} - 12)}{x (3 + \frac{5}{x})}) + lim_{x \to + \infty} (\csc (\frac{x (π + \frac{π}{x})}{4 x}))

= lim_{x \to + \infty} (\frac{\frac{3}{x} - 12}{3 + \frac{5}{x}}) + lim_{x \to + \infty} (\csc (\frac{π + \frac{π}{x}}{4 x}))

= \frac{0 - 12}{3 + 0} + \csc (\frac{π + 0}{4})

= - \frac{12}{3} + \csc (\frac{π}{4})

= - 4 + \sqrt{2}

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?