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If lim(xrarr1)((asin(x-1)+bcos(x-1)+4))/...

If `lim_(xrarr1)((asin(x-1)+bcos(x-1)+4))/(x^2-1)=2`, then `(a,b)` is equal to

A

`(2,3)`

B

`(a,-4),a in R`

C

`(3,-b),b in R`

D

`(4,-4)`

Text Solution

Verified by Experts

The correct Answer is:
D
We, have
`lim_(xto1)(asin(x-1)+bcos(x-1)+4))/(x^2-1)=2`
` rArr axx0+bxx1+4=0` and `lim_(xto1) (acos (x-1)-b(x-1))/(2x)=2`
` rArr b+4=0 and (a)/(2)=2`
`rArr a=4,b=-4`
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Section I - Solved Mcqs
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  2. If the equation of the normal to the curve y=f(x) at x=0 is 3x-y+3=0 t...

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  3. If lim(xrarr1)((asin(x-1)+bcos(x-1)+4))/(x^2-1)=2, then (a,b) is equal...

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  7. lim(nto oo) ((nsqrt(p)+nsqrt(q))/(2))^n,p,q,gt 0 equals

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  9. lim(xrarr0) (2^(|x|)e^(|x|)-|x|log(2)2-1)/(xtanx) is equal to

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  14. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)...

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  15. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  17. If P(x) is a polynomial such that P(x)+P(2x)=5x^2-18, then lim(xrarr3)...

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  18. If f(x) = lim(n->oo) sum(r=0)^n (tan(x/2^(r+1)) + tan^3 (x/2^(r+1)))/(...

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  19. Let f(x) is a polynomial function and f(alpha))^(2) + f'(alpha))^(2) =...

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  20. If f:[-1,1]toR and f'(0)=lim(ntooo)nf(1/n) and f(0)=0. Find the value ...

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