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Find k in R if f(x) = {:{((cos^2 x - sin...

Find `k in R` if `f(x) = {:{((cos^2 x - sin^2 x -1)/(sqrt(x^2+1) - 1), x ne 0), (k, x = 0):}` is continuous at 0.

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Consider the functions defined as follows, for x ne 0. In each case, w...

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  2. Find ainR so that f(x) = {:{(x^2, x ge0),(ax,x<0):} is continuous at 0...

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  3. Find k in R if f(x) = {:{((cos^2 x - sin^2 x -1)/(sqrt(x^2+1) - 1), x ...

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  4. Let f(x) = {:{((1-cosax)/(xsinx), x ne 0),(1/2, if x = 0):} If f is co...

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  5. Find the value of the constant k so that function f(x) = {{:((k cos ...

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  6. Examine the following functions for continuity: f(x) = {:{(x^n sin1/...

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  7. Examine the following functions for continuity: f(x) = {:{(x cos (1/...

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  8. Examine the following functions for continuity: f(x) = {:{((x-a) cos...

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  9. Examine the following functions for continuity: f(x) = {:{(e^(1//x),...

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

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  11. Find f(0) if the function defined as f(x) = {:{(log(1+x/a)-log(1-x/b))...

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  12. For what value of lambda is the function defined by f(x) = {:{lambda(x...

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  13. Show that the function defined by g(x) = x-[x] is discontinuous at al...

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  14. Show that the function f(x) = |sin x + cos x | is continuous at x = pi...

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  15. Extend the defination of the functionf(x) = (1-cos[7(x-pi)])/(5(x-pi)^...

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  16. Let f(x) = {:{(4x-3, if x<0),(4x + 3, if x ge 0):}. Is it a continuous...

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  17. Prove that the following functions are continuous at all points of the...

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  18. Prove that the following functions are continuous: cot x

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  19. Prove that the following functions are continuous: sec x

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  20. Prove that the following functions are continuous: sin^-1x

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