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lim(xto0) (e^(x^(2))-cosx)/(x^(2)) is e...

`lim_(xto0) (e^(x^(2))-cosx)/(x^(2))` is equal to

A

0

B

`1/2`

C

1

D

`3/2`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(x to0)lim(e^(x^(2))-cos x)/(x^(2))" "((0)/(0)"form")`
`=underset(x to 0)lim(2x^(x^(2))+sin x)/(2x)" "((0)/(0)"from")`
`=underset(x to 0)lim(2e^(x^(2))+sinx)/(2x)`
`=(2+0+1)/(2)=3/2`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 18-PAPER 2 (MATHEMATICS)
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  2. If int0^af(2a-x)dx=m and int0^af(x)dx=n, then int0^(2a) f(x) dx is equ...

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  3. lim(xto0) (e^(x^(2))-cosx)/(x^(2)) is equal to

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  4. If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy...

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  5. The Rolle's theorem is applicable in the interval -1le x le1 for the f...

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  6. The radius of a cylinder is increasing at the rate of 3ms^(-1) and its...

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  7. The probability that A speaks truth is (4)/(5), while this probability...

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  8. If A=[{:(6,8,5),(4,2,3),(9,7,1):}]then B =(A+A')/(2) is

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  9. If bar a,bar b and bar c are perpendicular ,bar c+bar a, bar b+bar c ...

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  10. The angle between the lines x^(2)+4xy+y^(2)=0 is

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  11. Let f(x) be given that f(x)={{:(,x,"if x is rational"),(,1-x,"if x is ...

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  12. If in the figure shown A=1 and B=0, then oupput will be

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  13. If vec a , vec b ,a n d vec c be non-zero vectors such that no tow...

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  14. Area of the region bounded by the curve y={{:(x^(2)",",x lt0),(x",",...

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  15. The critical points of the function f(x)=2sin ^(2)((x)/(6))+sin((x)/...

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  16. int (2)^(3){x} dx is equal to (where {.} denotes, fractional part of ...

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  17. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

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  18. lim(x to oo) (1-(4)/(x-1))^(3x-1) is equal to

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  19. The middle point of chord x+3y=2 of the conic x^(2)+xy-y^(2)=1, is

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  20. If the sum of n terms of an A.P is 2n + 3n^2 , find the r^(th) term

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