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Show that the function f(x)={:{(1+x ",...

Show that the function
`f(x)={:{(1+x ", " x le2","),(5-x", "x gt2):}` is not differentiable at x=2

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To show that the function \[ f(x) = \begin{cases} 1 + x & \text{if } x \leq 2 \\ 5 - x & \text{if } x > 2 \end{cases} ...
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Show tha the function f (x) = {{:(1+x"," if x le 2 ,), ( 5-x "," if x gt 2):} is not differentiable at x = 2 .

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The function f(x) = {(1 + x", when " x le 2),(5 -x ", when " x gt 2):} is

f(x)={{:(1+x, if x le 2),(5-x,ifx gt 2):} at x = 2 .

Show that the funcation f(x)={{:(3x-2",", " when ", x le0),(x+1",", " when ", x gt 0):} is discontinuous at x =0

If f(x)={:{(x^2", "x le 1),( x^2-x+1"," x gt1):} then show that f(x) is not differentiable at x=1 .

Find the value of k, so that the function f(x) = {(kx^2 + 5, if x le 1), (2, if x gt 1):} is continuous at x = 1

Find the value of k, so that the function f(x) = {(kx^2 + 5, if x le 1), (2, if x gt 1):} is continuous at x = 1

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NAGEEN PRAKASHAN-Continuity and Differentiability-Miscellaneous Exercise
  1. Show that the function f(x)={:{(1+x ", " x le2","),(5-x", "x gt2)...

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  2. Differentiate w.r.t. x the function. (3x^2-9x+5)^9

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  3. Differentiate w.r.t. x the functionsin^3x+cos^6x

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  4. Find dy/dx if y= (5x)^(3cos 2x)

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  5. sin^(-1)(xsqrt(x)),0 le x le 1

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  6. Differentiate w.r.t. x the function (cos^(-1)x/2)/(sqrt(2x+7)),-2<x<2

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  7. cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/...

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  8. (log x)^(log x),x gt1

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  9. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

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  10. (sinx-cosx)^((sinx-cosx)),(pi)/(4) ltx lt (3pi)/(4)

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  11. Differentiate w.r.t. x the function x^x+x^a+a^x+a^a ,for some fixed a...

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  12. Differentiate x^x^(2-3)+(x-3)^x^2 with respect to x :

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  13. Find (dy)/(dx),if y=12(1-cost), x=10(t-sint),-pi/2<t<pi/2

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  14. If y=sin^(- 1)x+sin^(- 1)sqrt(1-x^2) then find (dy)/(dx)

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  15. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

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  16. If (x-a)^2+(y-b)^2=c^2, for some c > 0, prove that ([1+((dy)/(dx))^2]^...

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  17. If cosy=xcos(a+y), with cosa!=+-1, prove that (dy)/(dx)=(cos^2(a+y...

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  18. If x=a(cost+tsint) and y=a(sint-tcost), find (d^(2)y)/(dx^(2)).

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  19. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

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  20. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

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  21. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

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