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If f(x) {: (=(8^(x) - 4^(x)-2^(x)+1)/(x...

If f(x) ` {: (=(8^(x) - 4^(x)-2^(x)+1)/(x^(2)) ", ... " x gt 0), ( = e^(x) sin x + pix + lambda . "In 4, ... " x le 0):}` is continuous at x = 0 , then : `lambda ` =

A

`4 log_e2`

B

`2log_e2`

C

`log_e2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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DISHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-Exercise-2 : Concept Applicator
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  2. The value of a for which the function f(x)=f(x)={((4^x-1)hat3)/(sin(x...

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  3. If f(x) {: (=(8^(x) - 4^(x)-2^(x)+1)/(x^(2)) ", ...

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  4. The function defined by f(x)={(((1)/(x^2+e^2-x))^(-1),xne2),(" "k"...

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  5. In the Mean Value theorem (f(b)-f(a))/(b-a)=f'(c) if a=0 , b =1/2 a...

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  6. Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x)i scon t inuou sa tx=...

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  7. Which of the following is true about f(x)={(((x-2))/(|x-2|)((x^2-1...

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  8. Let f be a continuous function on R such that f (1/(4n))=sin e^n/(e^...

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  9. if y=logx*e^((tanx+x^(2))), then (dy)/(dx) is equal to

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  10. Find the values of aa n db if f(x)={a+sin^(-1)(x+b),xgeq1x ,x<1 is di...

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  11. Which of the following functions is not differentiable at x=1?

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  12. If f(x)=(x)/(1+x)+(x)/((x+1)(2x+1))+(x)/((2x+1)(3x+1))+…"to "infty,the...

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  13. if f(x)=(x^2-4)|(x^3-6x^2+11x-6)|+x/(1+|x|)then set of points at which...

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  14. Number of point where function f(x) defined as f:[0,2pi] rarrR,f(x)={{...

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  15. If the function f(x)=[((x-2)^3)/a]sin(x-2)+acos(x-2),[dot] denotes the...

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  16. If g is the inverse function of fa n df^(prime)(x)=sinx ,t h e ng^(pri...

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  17. Which of the following function is not differentiable at x=0? f(x)=mi...

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  18. If y=[(tanx)^(tanx)]^(tanx),then at x=pi/4 , the value of (dy)/(dx)=

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  19. Given F(x)=f(x)phi(x) and f'(x)phi'(x)=c then prove that F''(x)/F(x)=...

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  20. Let f"":""RvecR be a function defined by f(x)""=""M in""{x""+""1,""...

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