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Determine if f defined by : f(x)={(x^2si...

Determine if f defined by : `f(x)={(x^2sin(1/x),,,, if x ne0),(0,,,, if x=0):}`is a continuous function?

A

f satisfies the conditions of Rolle's theorem on [-1,1]

B

f satisfies the conditions of Lagrange's Mean value theorem on [-1,1]

C

f satifies the conditions of Rolle's theorem on [0,1]

D

f satisfies the conditions of Lagrange's Mean value of theorem on [0,1]

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. The funtion f(x) = {:{(2x^2-1, if 1 le x le 4),(151-30x, if 4 < x le 5...

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  2. Let f(x) be a differentiable function and f'(4) = 5, then: underset(xr...

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  3. Determine if f defined by : f(x)={(x^2sin(1/x),,,, if x ne0),(0,,,, if...

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  4. If y=(1+x)(1+x^2)(1+x^4), then dy/dx at x = 1 is

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  5. The value of d/dx{tan^-1(cosx)} for x= 30 is equal to

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  6. If f(x) = {:{((x^2-(a+2)x+a)/(x-2), x ne2),(2,x=2):} is continuous at ...

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  7. Let g(x) = ((x-1)^3)/(log(x-1)) Find g(5).

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  8. Let y be an implict function of x defined by x^(2x) - 2x^x cot y -1 =0...

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  9. Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and ...

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  10. If 'f' is differentiable at x = a, find (underset(xrarra)lim(x^2f(a)-a...

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  11. If f: R rarr R is a function defined by: f(x) = [x] cos((2x-1)/2)pi, ...

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  12. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

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  13. If y = sec(tan^-1x), then dy/dx at x =1 is equal to

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  14. If g is te inverse of a function f and f'(x) = 1/(1+x^5) then g'(x) is...

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  15. If the function g(x) = {{:(k sqrt(x + 1)",", 0 le x le 3),(mx + 2",",3...

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  16. For x in R, f(x) = |log 2 - sin x| and g(x) = f(f(x)), then

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  17. A function f: R rarr R is defined as follows: f(x) = {:{(x,ifxle1),(...

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  18. If sqrtx+sqrty=4, then dy/dx is

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  19. Find dy/dx when x = 4t, y = 4/t

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  20. The funtion f(x) is defined as follows: f(x) = {:{(x^2+ax+b,0lex<2),...

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