Home
Class 12
MATHS
If lim(x to 0) (cos4x+acos2x+b)/(x^(4)) ...

If `lim_(x to 0) (cos4x+acos2x+b)/(x^(4))` is finite, find a and b using expansion formula. Also, find the limit.

Text Solution

AI Generated Solution

To solve the limit problem, we need to find the values of \( a \) and \( b \) such that \[ \lim_{x \to 0} \frac{\cos(4x) + a \cos(2x) + b}{x^4} \] is finite. We will use the Taylor series expansion for \( \cos(x) \). ...
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.1|10 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

If ("lim")_(xvec0)(cos4x+acos2x+b)/(x^4) is finite, find aa n db using expansion formula.

If lim_(x rarr 0) (cos4x+a cos2x+b)/x^4 is finite then the value of a,b respectively

Evaluate lim_(x to 0) ("sin"^(2) 4x)/(x^(2))

If lim_(x to 0) ("sin" 2x + a "sin" x)/(x^(3)) =b (finite), then (ab)^(2) equals…..

Evaluate the following limits : Lim_(x to 0) (1-cos 2x)/(x^(2))

Evaluate the following limits : Lim_(x to 0) (cos Ax - cos Bx)/(x^(2))

Evaluate the following limits : Lim_(x to 0) (1-cos 4x)/(x^(2))

Evaluate the following limits : Lim_(x to 0) (1- cos x)/(x^(2))

Evaluate the limits using the expansion formula of functions lim_(x->0) (sinx+log(1-x))/x^2

Evaluate the following limits : Lim_(x to 0) (sin 3x cos 2x)/(sin 2x)