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If lim(x to 0)kxcosecx=lim(x to 0)xcosec...

If `lim_(x to 0)kxcosecx=lim_(x to 0)xcoseckx`, show that `k=pm1`.

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-REVISION EXERCISE
  1. lim(x->1)(x^4-3x^2+2)/(x^3-5x^2+3x+1)

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  2. Evaluate the following limits lim(x to 1)(1/(x-1)-(3(x-2))/(x^(3)-3x^(...

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  3. Evaluate the following limit: (lim)(x->1)(1/(x^2+x-2)-x/(x^3-1))

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  4. lim(x->3) {x^3-7x^2+15x-9}/{x^4-5x^3+27x-27} is equal to:

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  5. Evaluate: lim(xto0)((1+x)^(6)-1)/((1+x)^(2)-1)

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  6. Evaluate : ("lim")(xvecoo)(a x^2+b x+c)/(dx^2+e x+f)dot

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  7. The value of lim(xto oo)(sqrt(3x^2-1)+sqrt(2x^2-1))/(4x+3), is

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  8. Evaluate the following limits : lim(x to infty)(sqrt(x^(2)+x+1)-sqrt(...

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  9. Given f(x)=(ax+b)/(x+1), lim(x to oo)f(x)=1 and lim(x to 0)f(x)=2, th...

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  10. If lim(x to 0)kxcosecx=lim(x to 0)xcoseckx, show that k=pm1.

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  11. lim(x->0)(2sinx^0-sin2x^0)/(x^3)

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  12. If alpha, beta are the zeroes of ax^(2)+bx+c, then evaluate : lim(x ...

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  13. Find the derivative of the following functions (it is to be understand...

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  14. Find the derivative of (x^n-a^n)/(x-a)for some constant a.

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  15. Differentiate each of the following from first principle: tansqrt(x)

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  16. Find the derivative : x^(2)cosx

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  17. Find the derivative of s in x3 from first principles.

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  18. If f(x)=x^(2)-3x+4, find the value of x for which the derivative is ze...

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  19. If f(x)=x^(2)-4x+3, find the value of x for which the derivative is 2.

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  20. If f(x)=x^(3)tanx+3x^(4)sinx, find its derivative at x = 0 and x = pi/...

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