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lim(x->0) (tan x - sin x)/(x^3) is equal...

`lim_(x->0) (tan x - sin x)/(x^3)` is equal to

A

0

B

1

C

`(1)/(2)`

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(x to 0)(tanx- sin x)/(x^(3))`
`= lim_(x to 0) (tan x(1- cos x))/(x^(3))`
`= lim_( x to 0) (tan x)/(x) *( 2 sin ^(2)(x//2))/(4(x//2)^(2))=(1)/(2)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 07-PAPER 2( MATHEMATICS)
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  3. Find the equation of a circle with centre (h, k) and touching the...

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  4. Angle between tangents drawn to circle x^2+y^2=20 from the point (6,...

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  5. The valume of the parallelopiped whose coterminous edges are hati-hatj...

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  6. Consider the inequalities x(1)+x(2) le,2, 2x(1)+5x(2) ge 10, x(1),x(2)...

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  7. The switching function for the following network is

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  8. Gien that X is discrete random variable which take the values, 0,1,2 a...

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  9. The degree of the differential equation (d^(3)y)/(dx^(3))+2 "sin"(dy)/...

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  10. if x=a cos^(4) theta, y= a sin^(4) theta, "then" (dy)/(dx)"at" theta=(...

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  11. For any square matrix A,A A^(T) is a

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  12. If the pair of straight lines xy - x - y +1=0 & the line ax+2y-3=0 are...

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  13. If y=sqrt(x s inx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)...

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  14. The differential equation, obtained on eliminating A and B from the eq...

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  15. The equation sin^-1x-cos^-1x=cos^-1(sqrt3/2) has

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  16. lim(x->0) (tan x - sin x)/(x^3) is equal to

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  17. If 2 cos x ne 2 sin, x then the general solution of sin^(2)x-cos2x=2 s...

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  18. The equation of the plane passing through the points (1,2,3), (-1,4,2)...

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  19. The eqution of the plane which meets the axes in A,B,C such that the c...

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  20. If a=hati-hatj-hatk and b= lambda hati-3hatj+ hatk and the orthogonal ...

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