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Evaluate: ("lim")(xvec2a^+)((e^x I n(2^(...

Evaluate: `("lim")_(xvec2a^+)((e^x I n(2^(x-1))-(2^x-1)^xsinx)/(e^(x I nx)))^(1/x)`

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RESONANCE DPP-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^...

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  2. Evaluate : ("lim")(xvec2a^+)(sqrt(x-2a)+sqrt(x)-sqrt(2a))/(x^2-4a^2)

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  3. Evaluate: ("lim")(xvec2a^+)((e^x I n(2^(x-1))-(2^x-1)^xsinx)/(e^(x I n...

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  4. If f^(prime)(k)=l ,t h e nl= 0 (b) 4/5 (c) pi/2 (d) (16)/5

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  5. f^(prime)(l+3)= 0 (b) 2/5 (c) -2/5 (d) -4/5

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  6. Comprehension (for Q. No. 1 to 3) Let f(x)=sin^(-1)(1-x^2)/(1+x^2)+tan...

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  7. Solve for x , if [cos^(-1)x]=[sin^(-1)x] (where [.] represents greates...

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  8. underset(x to0)(lim)((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " th...

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  9. Which of the following is true? pi/3>tan^(-1)pi/3 (b) pi/3<tan^(-1)pi...

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  10. Let f(x)=[(sinx)/x]+[(2sin2x)/x]+.....+[(10sin10 x)/x] (where [.] is t...

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  11. The sum of the series x/(1)+(2x^2)/(2)+(3x^3)/(3)+ is x e^x b. -x e...

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  12. If a x^2+2h x y+b y^2=0, then (dy)/(dx) is equal to y/x (b) x/y (c) ...

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  13. If f(x)=(log)x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e ...

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  14. Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt)=2 and x=3 at t=0, then (dx)/...

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  15. Let g is the inverse function of fa n df^(prime)(x)=(x^(10))/((1+x^2))...

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  16. If x=(1+t)/(t^3),y=3/(2t^2)+2/t ,t h e nx((dy)/(dx))^3-(dy)/(dx) is eq...

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  17. If u=f(x),v=g(x), then the value of D^*(udotv) is (D^*u)v+(D^*v)u b. u...

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  18. Let f(x)={((x-4)/(|x-4|)+a ,x<4),(a+b ,x=4),((x-4)/(|x-4|)+b ,x >4):} ...

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  19. If f(x)=x^3+bx^2+cx+d and 0 < b^2 < c, then in (-oo,oo), (a) f(x) is...

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  20. The point(s) of minimum of function, f(x)=4x^3-x|x-2|,x in [0,3] is x=...

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