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Consider the function f(x)={(1-x,x<0),(1...

Consider the function `f(x)={(1-x,x<0),(1,x=0),(1+x,x>0):}`
Draw a rough sketch of `f(x)` .

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MAXIMUM PUBLICATION-CONTINUITY & DIFFERENTIABILITY-EXAMPLE
  1. If x=asec^3theta and y=atan^3theta Show that ((d^2y)/(dx^2))(theta=p...

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  2. Consider the function f(x)={(1-x,x<0),(1,x=0),(1+x,x>0):} Complete t...

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  3. Consider the function f(x)={(1-x,x<0),(1,x=0),(1+x,x>0):} Draw a rou...

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  4. Consider the function f(x)={(1-x,x<0),(1,x=0),(1+x,x>0):} Draw a rou...

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  5. Consider the equation sqrt(1-x^2)+sqrt(1-y^2)=a(x-y) Simplify the ...

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  6. Consider the equation sqrt(1-x^2)+sqrt(1-y^2)=a(x-y) Prove that dy...

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  7. Match the following.

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  8. If y=e^(acos^-1x) , then show that (1-x^2)y2-xy1-a^2y=0

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  9. Match the following.

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  10. Differentiate the following y=1/(5x^2+3x+7)

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  11. Differentiate the following y=3cosec^4(7x)

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  12. Differentiate the following y=e^(2log tan5x)

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  13. Consider f(x)={((x^2-x-6)/(x+2),x ne-2),(-5,x=-2):} Find f(-2)

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  14. Consider f(x)={((x^2-x-6)/(x+2),x ne-2),(-5,x=-2):} Check whether th...

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  15. If f(x)=sin(logx) , prove that x^2y2+xy1+y=0

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  16. Establish that g(x)=1-x+absx is continious at origin.

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  17. Check whether h(x)=abs(1-x+absx) is continious at origin.

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  18. Find dy/dx of x=sqrt(a^(sin^-1t) y=sqrt(a^(cos^-1t)

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  19. Find dy/dx of y=cos^-1frac(1-x^2)((1+x^2)), 0<x<1

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  20. Find dy/dx of y=sin^-1 2xsqrt(1-x^2) (-1)/sqrt2<x<1/sqrt2

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