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(lim(xto oo) ((x+3)/(x+1))^(x+1) is equa...

`(lim_(xto oo) ((x+3)/(x+1))^(x+1)` is equal to

A

`e^(2)`

B

`e^(3)`

C

`e`

D

`e^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(x to oo)(lim)((x+3)/(x+1))^(x+1)`
`=underset(xto oo)(lim)(1+(2)/(x+1))^((x+1)/(2)*2)=e^(2)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 04-PAPER 2 (MATHMATICS)
  1. Shaded region is represented by

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  2. If the normal to the curve y=f(x) at the point (3,4) makes an angle (3...

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  3. (lim(xto oo) ((x+3)/(x+1))^(x+1) is equal to

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  4. The equation of the plane passing through (3,2,-1) and normal tot the ...

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  5. For the Booleann function f(x(1),x(2),x(3))=(x(1)*x(2))+x(3), value of...

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  6. The volume of the parallelopiped, if a=3hati,b=5hatj and c=4hatk are c...

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  7. Find the ratio in which the line joining (2,4,5) and (3,5,4) is divide...

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  8. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

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  9. The differential coefficient of f(sin x) with respect to x, where f(x)...

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  10. Gas is being pumped into a a spherical balloon at the rate of 30 ft^(3...

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  11. The vectors which is/are coplanar with vectors hati+hatj+2hatk and hat...

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  12. if the function f:R to R be defined by f(x)=tanx-x, then f(x) always

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  13. int(0)^(pi)(xdx)/(1+sinx) is equal to

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  14. If f(x)=x+1/x ,\ \ x >0 , then its greatest value is -2 (b) 0 (c) 3...

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  15. The sum to infinity of the series 1+2/3+6/(3^2)+(10)/(3^3)+(14)/(3^...

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  16. A straight line passes through the points (5,0) and (0,3). The length ...

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  17. The ratio by which the line 2x + 5y -7=0 divides the straight line joi...

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  18. Let A (2,-3) and B(-2,1) be vertices of a triangle ABC. If the centroi...

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  19. A hyperbola passes through a focus of the ellipse x^2/169 + y^2/25=1. ...

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  20. If A=[(1,-2,1),(2,1,3)] and B=[(2,1),(3,2),(1,1)] then (AB)' is equal ...

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