help@askiitians.com

+91-93193 64476

Differential Calculus> Find the value of a for which the limit o...

question mark

Find the value of a for which the limit of function exists at x = 0.
f(x) = (1-cos4x)/x², x
f(x) = a, x = 0
f(x) = (x)^1/2/((16 + x^1/2)^1/2 – 4), x > 0

Lovey , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Ans:
Since the limit of function exist at zero. So at x = 0
LHL = f(0) = RHL
$LHL = \lim_{x\rightarrow 0}\frac{1-cos4x}{x^{2}}$
Apply L’Hospital rule
$LHL = \lim_{x\rightarrow 0}\frac{4sin4x}{2x}$
$LHL = \lim_{x\rightarrow 0}\frac{2sin4x}{x}$
$LHL = \lim_{x\rightarrow 0}\frac{2.4cos4x}{1} = 8$
$LHL = a$
$a = 8$

Approved

Last Activity: 11 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?

differential calculus

1 Answer Available

Last Activity: 3 Years ago

Find dy/DX when y=x^sinx+sin-1√x.

Please give me the solution of this problem.

differential calculus

1 Answer Available

Last Activity: 3 Years ago

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

differential calculus

1 Answer Available

Last Activity: 3 Years ago

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

View all Questions