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Find lim(x->0)(sin(pisin^2(x))/x^2)...

Find `lim_(x->0)(sin(pisin^2(x))/x^2)`

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lim_(x rarr 0) (sin(pi sin^2 x))/x^2=

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Evaluate lim_(xto0) sin(picos^(2)x)/(x^(2)).

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If L=lim_(x->0)(sin2x+asinx)/(x^3) is finite, then find the value of a

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lim_(xrarr0)sin(picos^2x)/x^2 is equal to :

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Find the intervals in which the follwing functions are increasing or d...

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  2. Find the intervals in which the follwing functions are increasing or d...

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  3. Find lim(x->0)(sin(pisin^2(x))/x^2)

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  4. lim(x to 0) (1-cosx)/x^2 = ?

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  5. If f(x)=ax^3+bx^2+cx+d has local extrema at two points of opposite si...

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  6. Prove that if 2a0^2lt15a all roots of x^5-a0x^4+3ax^3+bx^2+cx+d=0 can...

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  7. Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where ...

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  8. Let a+b=4, where a gt 2 and let g(x)be a differentiable function. If ...

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  9. On the curve x^3=12y the abscissa changes at a faster rate than the or...

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  10. A spherical iron ball 10 cm in radius is coated with a layer of ice of...

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  11. The function f(x)=tan^(-1)x-x decreases in the interval

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  12. The function f(x)=2log(x-2)-x^2+4x+1 increases in the interval

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  13. The function f(x)=sin^4x+cos^4x increasing if :

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  14. The length of the longest interval in which the function 3sinx-4sin^3x...

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  15. The function f(x) =tan^(-1)(sinx+cosx) is an increasing function in

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  16. The function f defined by f(x)=4x^4-2x+1 is increasing for

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  17. The value of a for which the functionf(x)=asinx+1/3sin3x has an extrem...

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  18. xgt0,ygt0 and x+y=1. The minimum value of xlogx+ylogy is

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  19. The minimum value of 2log10x-logx0.01. xgt1, is

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  20. The maximum slope of the curve y=-x^3+3x^2+2x-27 is

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