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`("lim")_(x -> 0)((1+tanx)/(1+sinx))^(cos e cx)` is equal to (a)e (b) `1/e` (c) 1 (d) none of these

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)...

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  2. ("lim")(xvecoo)[(e/(1-e))(1/e-x/(1+x))]^xi s e^((1-e)) (b) e^(((1-e)...

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  3. ("lim")(x -> 0)((1+tanx)/(1+sinx))^(cos e cx) is equal to (a)e (b...

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  4. ("lim")(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) ...

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  5. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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  6. "F i n d"(dy)/(dx)"if"y=tan^(-1)((sqrt(1+x^2)-1)/x), where x!=0

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  7. If y=sin^(-1)((2x)/(1+x^2)), then find (dy)/(dx)

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  8. If y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))ltxlt1 /(sqrt(3)), then f...

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  9. Find (dy)/(dx) for the functions: y=(x+sinx)/(x+cosx)

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  10. Find the derivative of the function given by f(x)=(1+x)(1+x^2)(1+x^4)(...

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  11. Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x...

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  12. Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) ...

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  13. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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  14. If y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2)),="" then="" find="" (dy)/(d...

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  15. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^-1 (2) -((d^2y)/(dx^2))^-1...

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  16. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

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  17. let f(x)=2+cosx for all real x Statement 1: For each real t, there ex...

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  18. Differentiate the function with respect to x using the first principle...

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  19. Match the following: List - I, List - II Let y(x)=cos(3cos^(-1)x) ...

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  20. Differentiate the function with respect to x using the first principle...

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