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The graph of function y=f(x) has a uniqu...

The graph of function y=f(x) has a unique tangent at `(e^a,0)`, through which the graph passes, then
`lim_(xrarre^a)(log(1+7f(x))-sin(f(x)))/(3f(x))` is equal to

A

1

B

2

C

7

D

none of these

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The correct Answer is:
B
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Evaluate lim(xrarr0) tan(2x )/x

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  2. Evaluate lim(xrarra)(2-a/x)^("tan"(pix)/(2a))

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  3. The graph of function y=f(x) has a unique tangent at (e^a,0), through ...

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  4. Evaluate lim(nrarrinfty)([x]+[2x]+[3x]+......+[nx])/(n^2) where [.] d...

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  5. Evaluate lim(xrarr0)(int0^(x^2) costdt)/(xsinx)

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  6. Evaluate lim(xrarr0)(x-int0^(x) cost^2dt)/(x^3-6x)

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  7. Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/x)

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  8. If alpha and beta be the roots of the quadratic equation ax^2+bx+c=0 t...

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  9. Let a=min{x^2+2x+3, x in R} and b=lim(thetararr0)(1-costheta)/(theta^2...

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  10. If f(x)={(2x+3, "when x" lt 0),(0, "when x"=0),(x^2+3, "when x"gt 0):}...

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  11. Let y=f(x) be defined parametrically as y=t^2+t|t|, x=2t-|t|, t in R, ...

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  12. Let f(x) be a continuous function defined for 1 le x le 3. If f(x) tak...

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  13. Find the points points of discontinuity of y=1/(u^2+u-2) where u=1/(x-...

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  14. If f(x)=[x], where [.] denotes greatest integer function. Then check t...

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  15. Let f(x)={({1+|sinx|}^(a//|sinx|), -pi//6ltxlt0),(b, x=0),(e^(tan2x...

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  16. Discuss the continuity of f(x)=[tan^(-1)x]

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  17. Examine the function, f(x)={(x-1, x lt 0),(1//4, x=0), (x^2-1, xg...

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  18. Show the function, f(x)={((e^(1//x)-1)/(e^(1//x)+1), "when x" le 0),...

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  19. A function f(x) is defined by, implies f(x)=f(x)={(([x^2]-1)/(x^2-1)...

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  20. Discuss the continuity of the function, f(x)=lim(nrarrinfty)(log(2+x)...

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