Home
Class 12
MATHS
Evaluate lim(xto0) (8)/(x^(8)){1-"cos"(x...

Evaluate `lim_(xto0) (8)/(x^(8)){1-"cos"(x^(2))/(2)-"cos"(x^(2))/(4)+"cos"(x^(2))/(2)"cos"(x^(2))/(4)}.`

Text Solution

Verified by Experts

The correct Answer is:
`1//32`
`underset(xto0)lim(8(1-"cos"(x^(2))/(4))(1-"cos"(x^(2))/(2)))/(x^(8))`
`=underset(xto0)lim(8xx2"sin"^(2)(x^(2))/(8)xx2"sin"^(2)(x^(2))/(4))/(x^(8))`
`=underset(xto0)lim(32)/(64xx16).("sin"^(2)(x^(2))/(8))/(x^(4)/(64)).(2"sin"^(2)(x^(2))/(4))/(x^(4)/(16))`
`=1/32`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.6|9 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.7|7 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.4|5 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate: (lim)_(x rarr0)(8)/(x^(8)){1-cos((x^(2))/(2))-cos((x^(2))/(4))+cos((x^(2))/(2))cos((x^(2))/(4))}

Evaluate lim_(xto0)(1-cos2x)/(1-cos4x)

Evaluate lim_(xto0) (1-cos(1-cosx))/(x^(4)).

Evaluate lim_(xto0) (xtan2x-2xtanx)/((1-cos2x)^(2)).

Evaluate the following limits (i) lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)] (ii) lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta)) (iii) lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x) (iv) lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))

lim_(xto0) (1)/(x^12){1-cos (x^2/2)-cos (x^4/4)+cos (x^2/2) cos (x^4/4)} is equal to

Evaluate lim_(xto0)x^(3)"cos"2/x .

Evaluate lim_(xto0)(int_(0)^(x^(2))cos^(2)tdt)/(x sin x)

Evaluate: lim_(xto oo)(2x^(2)-2x-sin^(2)x)/(3x^(2)-4x+cos^(2)x)