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If lim(x→0) ​ (x^asin^b x)/(s...

If `lim_(x→0) ` ​ `(x^asin^b x)/(sin(x^c))`, where a , b , c in R ~{0},exists and has non-zero value. Then, `

A

0

B

`pi//2`

C

`pi`

D

`2pi`

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xto0)lim(x^(a)sin^(b)x)/(sinx^(c))=underset(xto0)limx^(a)((sinx)/(x))^(b)((x^(c))/(sinx^(c)))x^(b-c)=underset(xto0)limx^(a+b-c)`
This limit will have non-zero value of `a+b=c.`
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CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
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  13. The value of ("lim")(x->a)sqrt(a^2-x^2)cot(pi/2sqrt((a-x)/(a+x))) is (...

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  14. lim(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest...

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  15. The value of lim(xto0) (1-(cosx)sqrt(cos2x))/(x^(2)) is

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  16. lim(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) is equal to

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  17. The value of lim(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is (a)4 (b) ...

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  18. lim(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 ...

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  20. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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