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lim(xrarr0) (sin(picos^2x))/(x^2) equals...

`lim_(xrarr0) (sin(picos^2x))/(x^2)` equals

A

`-pi`

B

`pi`

C

`(pi)/(2)`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
B
We have ,
`lim_(xto0) (sin(picos^2x))/(x^2)`
` =lim_(xto0) (sin(pi-picos^2x))/(x^2)`
` =lim_(xto0) (sin(pisin^2x))/(pisin^2x)xx(pisin^2x)/(x^2)=1xxpixx(1)^2=pi`
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OBJECTIVE RD SHARMA-LIMITS-Section I - Solved Mcqs
  1. For x in R , lim(xrarr oo) ((x-3)/(x+2))^x =

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  2. lim(xrarr0) (sin(picos^2x))/(x^2) equals

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  3. The integer n for which lim(x rarr 0) ((cos x-1) ( cos x - e^x))/x^n i...

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  4. A function f : RR rarr RR is such that f(1) = 3 and f'(1) = 6. Then li...

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  5. lim(xrarr oo) (a^nb^n)/(a^n-b^n), where 1lt b lt a , is equal to

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  6. lim(xrarr oo) (4^(1//n)-1)/(3^(1//n)-1) is equal to

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  7. lim(x->oo)(sqrt(x^4+ax^3+3x^2+b x+2)-sqrt(x^4+2x^3+cx^2+3x-d))=4

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  8. if lim(x->0)(1+a x)^(b / x)=e^2, where a and b are natural numbers, th...

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  9. lim(nto oo) (2^n+5^n)^(1//n) is equal to

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  10. lim(xrarr oo) (log[x])/(x) , where [x] denotes the greatest integer le...

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  11. lim(xrarr oo) (logx)/([x]) , where [.] denotes the greatest integer fu...

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  12. lim(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the grea...

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  13. If a .lim(xrarr 1) x^(1//1-x)+b=e^(-1)(a ge 1,bge 0) , then

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  14. lim(xrarr -1) (cos 2 -cos 2x)/(x^2-|x|) is equaol to

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  15. Lim(x->oo) ((x/(x+1))^a + sin (1/x))^x is equal to

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  16. If {x} denotes the fractional part of x, then underset(x to 0)(lim) ({...

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  17. If {x} denotes the fractional part of x, then lim(xrarr1) (x sin {x})/...

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  18. lim(xrarr1) (sinsqrt(x))/(sqrt(sinx)) is equal to

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  19. If alpha and beta are roots of the equation ax^2+bx +c=0, then lim(xr...

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  20. If f(x)=1/3{f(x+1)+5/(f(x+2))} and f(x)>0 for all x in R, then lim(x->...

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