Question

solve the limit of the function f(x)=sin5x/sinx if x --> pi

Accepted Answer

We have to find the value of lim x--> pi[ sin 5x / sin x]
We see that substituting x with pi gives us the form 0/0 which is indeterminate. We can use therefore use l'Hopital's rule and use the derivative of the numerator and the denominator
lim x--> pi [sin 5x / sin x]
=> lim x--> pi [ 5* cos 5x / cos x]
substtuting x = pi , now gives
(5*-1)/ (-1)
=> 5
The required value of lim x--> pi[ sin 5x / sin x] is 5.

Answer

We'll create the remarcable limits:
lim sin x/x = 1, if x->0
We'll re-write the function:
lim [(sin 5x)/5x]*[(5x)/sin x] = lim [(sin 5x)/5x]*lim [(5x)/sin x]
lim [(sin 5x)/5x]*lim [(5x)/sin x] = 1*lim [(5x)/sin x] 
 1*5lim [(x)/sin x]  = 1*5 = 5
The limit of the given function is : lim sin5x/sinx = 5, if x -> pi.

Calculus

solve the limit of the function f(x)=sin5x/sinx if x --> pi

Expert Answers

We’ll help your grades soar

Related Questions

Determine the limit of the function (sin5x-sin3x)/x, x-->0

Evaluate the limit of the function ln(1+x)/(sinx+sin3x) x-->0

Evaluate the limit of the fraction (f(x)-f(1))/(x-1), if f(x)=1+2x^5/x^2? x->1

Verify if limit of ln(1+x)/x is 1, x-->0

Prove that limit of the function (a^x-1)/x=lna,x->0,using two methods.