If the function f(x) = (cos (sin x) - cos x)/(x⁴) is continuous at each point in its domain and f(0) = 1/k, then k is _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 17 Mar, Morning shift · Q36

JEE Main 202117 Mar, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

If the function

f(x) = {{\cos (\sin x) - \cos x} \over {{x^4}}}

is continuous at each point in its domain and

f(0) = {1 \over k}

, then k is ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 · 17 Mar, Morning shift · Q36

JEE Main 202117 Mar, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

If the function

f(x) = {{\cos (\sin x) - \cos x} \over {{x^4}}}

is continuous at each point in its domain and

f(0) = {1 \over k}

, then k is ____________.

Your answerType your answer. Integers and decimals are accepted.