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Show that the function f:RRrightarrowRR ...

Show that the function `f:RRrightarrowRR` defined by `f(x)={(x^2-frac[1][x^2], xne0),(0, x=0):}` is onto but not one-to-one.

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f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

Show that the function f: R rarr R given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is not one - one

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Show that f(x)={(x sin frac{1}{x}, xne0),(o,x=0):} is continuous at x=0

Show that the function f:R to R defined by f(x)=(x)/(x^(2)+1) is neither one-one nor onto.

Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if "x!=0),(0" , if "x=0):} is continuous at x =0

Show that the function f : R rarr R defined as f(x) = x^(2) is neither one-one nor onto.

Find the value of a, so that the function f(x) is defined by f(x)={{:((sin^(2)"ax")/(x^(2))", "x!=0),("1, "x=0):} may be continuous at x=0.

Find the value of a such that the function f defined by f(x)={{:((sinax)/(sinx), "if", x ne 0),((1)/(a), "if", x=0):} is continuous at x=0

Show that f(x)={(xsinfrac{1}{x},xne0),(0,x=0):} is not differentiable x=0

USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. What is the number of independent constants that occur in the general ...

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  2. Show that the relation R on Z – {0} defined by R={(m,n)|frac[m][n] is ...

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  3. Show that the function f:RRrightarrowRR defined by f(x)={(x^2-frac[1][...

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  4. Solve for x, cos^(-1)x +sin^(-1)((x)/(2)) =(pi)/(6).

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  5. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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  6. A diet for a sick person must contain at least 4000 units of vitamins,...

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  7. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  8. Find inverse of the following matrices by elementary row/column operat...

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  9. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  10. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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  11. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  12. Test differentiability and continuity of the following functions. |1...

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  13. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  14. Find dy/dx if y = x cot^(-1) (x/y)

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  15. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

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  16. Show that 2sinx+3tanxgt3x for all xin(0,frac[pi][2])

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  17. Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.

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  18. int(pi/5)^(3pi/10) (sinxdx)/(sinx+cosx)

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  19. Find the area of the region bounded by y=6x-x^2x-axis and between ordi...

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  20. Solve : (dy)/(dx)= sin(x+y)+cos(x+y)

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