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Let g(x)=((x-1)^(n))/(logcos^(m)(x-1)),0...

Let `g(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2` m and n integers, `m ne0, n gt0` and. If `lim_(xrarr1+) g(x)=-1`, then

A

n= 1, m = 1

B

n = 1, m = -1

C

n = 2, m = 2

D

n gt 2, m = n

Text Solution

Verified by Experts

The correct Answer is:
C
We have `underset(xrarr1^(+))(lim)((x-1)^(n))/(logcos^(m)(x-1))=-1`
`rArr" "underset(hrarr0)(lim)(h^(n))/(m(log cos h))=-1`
`rArr" "underset(hrarr0)(lim)(nh^(n-1)cos h)/(m((sinh)/(h)))=1" (Applying L'Hospital Rule)"`
`rArr" "underset(hrarr0)(lim)(nh^(n-2))/(m)=1`
`rArr" "n=2 and m=2`
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CENGAGE-LIMITS-Single Correct Answer Type
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  10. The value of lim(x rarr 0) (1-cos2x)/(e^(x^(2))-e^(x)+x) is

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  14. If F:R rarr R be a differentiable function at x = 0 satisfying f(0)=0 ...

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