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Prove that sin1>cos(sin1)dot Also, show ...

Prove that `sin1>cos(sin1)dot` Also, show that the equation `sin("cos"(sinx))=cos("sin"(cosx))` has only one solution in `[0,pi/2]dot`

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Show that 5xlt=8sinx-sin2xlt=6x for 0lt=xlt=pi/3dot

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  2. Discuss the number of roots of the equation e(k-xlogx)=1 for different...

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  3. Prove that sin1>cos(sin1)dot Also, show that the equation sin("cos"(si...

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  4. Pa n dQ are two points on a circle of centre C and radius alpha . The ...

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  5. If f(x)=2/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^2+x+1)+(lambda^2-5...

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  6. Let f(x)={(2-|x^2+5x+6|,x!=-2),(a^2+1,x=-2):} then value of 'a' so tha...

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  7. If A >0,B >0 and A+B=pi/3, the maximum value of tanAtanB is

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  8. f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasi...

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  9. If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(''')(a)>0, then at x=a...

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  10. The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot The...

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  11. Iff(x)={sin^(-1)(sinx),x >0, pi/2,x=0,tcos^(-1)(cosx),x<0

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  12. f: R to R ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot ...

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  13. Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^...

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  14. If f: RtoRa n dg: RtoR are two functions such that f(x)+f^(primeprime)...

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  15. Let h(x)=x^(m/n) for x in R , where m and n are odd numbers where 0<...

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  16. Find the number of points of maxima and minima of the function. f(x)=1...

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  17. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

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  18. The circle x^2+y^2=1 cuts the x-axis at Pa n dQdot Another circle with...

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  19. let f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2) if x is 0 to 1 and f(x)=2x-3 if...

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  20. A cubic f(x) vanishes at x= -2 and has relative minimum and maximum a...

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