AIMAL
AIMAL
04-04-2017
Mathematics
contestada
limit question: lim x-->pi ((e^sinx)-1)/(x-pi)
Respuesta :
LammettHash
LammettHash
13-04-2017
[tex]\displaystyle\lim_{x\to\pi}\dfrac{e^{\sin x}-1}{x-\pi}[/tex]
Notice that if [tex]f(x)=e^{\sin x}[/tex], then [tex]f(\pi)=e^{\sin\pi}=e^0=1[/tex]. Recall the definition of the derivative of a function [tex]f(x)[/tex] at a point [tex]x=c[/tex]:
[tex]f'(c):=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}[/tex]
So the value of this limit is exactly the value of the derivative of [tex]f(x)=e^{\sin x}[/tex] at [tex]x=\pi[/tex].
You have
[tex]f'(x)=\cos x\,e^{\sin x}\implies f'(\pi)=\cos\pi\,e^{\sin\pi}=-1[/tex]
Answer Link
VER TODAS LAS RESPUESTAS ( 46+ )
Otras preguntas
which of reduces the risk of data exposure between containers on a cloud platform?
Which of the following is most likely to reduce the kinds of group biases that exist in face-to-face groups? A. crowd psychology B. herd mentality C. crowdsourc
100 points again 100 points again 100 points again
which of reduces the risk of data exposure between containers on a cloud platform?
Review pages 2 and 3. click or tap the ONE underlined line on these pages that supports the inference that Beatrice thinks Benedick has a fickle nature.
An equilateral triangle has sides 10 cm in length. Calculate the perpendicular height of the triangle. (to nearest mm) Help please
A 10-year-old client with asthma is prescribed 2 mg of albuterol syrup four times per day. the syrup is available as a formulation of 2 mg/5 ml. how many millil
the american musical form that developed between 1880-1900 and spoke of personal feelings of suffering, hard times, lust, and love is:
Which set of numbers can represent the side lengths, in inches, of an acute triangle? 4, 5, 7 5, 7, 8, 6, 7, 10 7, 9, 12
A social worker earns an average bi-weekly net pay of $1,465.87. Which compound inequality correctly shows the amount of money, m, the social worker can spend i