Limits & Continuity: If lim_xto2(tan ((x-2) (x^2+(k-2)x-2k ) ))/(x^2-4x+4)=5 , then k is… | JEE Main 2014 | Yukti Vault

Yukti Vault

JEE Main 2014 (Online) 11th AprilQuestion 1

If $\lim_{x\to2}\frac{\tan\left((x-2)\left(x^2+(k-2)x-2k\right)\right)}{x^2-4x+4}=5$, then $k$ is equal to :

Limits & Continuity

$0$$1$$2$$3$✓ Correct answer

Solution

$x^2+(k-2)x-2k=(x-2)(x+k)$, so the argument is $(x-2)^2(x+k)$ and the limit is $2+k=5$, $k=3$.

More from Limits & Continuity

If f(x)=begincases(a|x|+x^2-2(sin|x|)(cos|x|))/(x), & xne0\\ b, & x=0endcases is continuous at x=0 , then…
lim_ntoinfty \ (2^(1)/(2)-2^(1)/(3) ) (2^(1)/(2)-2^(1)/(5) )cdots (2^(1)/(2)-2^(1)/(2n+1) ) \ is equal to
If f(x) be a differentiable function such that f(9)=9 and f'(9)=4 , then lim_xto9fracsqrt(f(x))-3sqrt(x)-3…
Let f:mathbbRtomathbbR be a function defined as f(x)=asin ((pi[x])/(2) )+[2-x] , ainmathbbR , where [t] is…
Let f:mathbfRtomathbfR be a continuous function such that f(3x)-f(x)=x . If f(8)=7 , then f(14) is equal to :
The value of lim_ntoinftyfrac1+2-3+4+5-6+ldots+(3n-2)+(3n-1)-3nsqrt2n^4+4n+3-sqrtn^4+5n+4 is
If lim_xto0fracax- (e^4x-1 )ax (e^4x-1 ) exists and is equal to b , then the value of a-2b is \_\_\_\_\_\_ .
Let f(x)=begincases3x, & x 2endcases , where [ . ] denotes greatest integer function. If alpha and beta are…