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Let f(x) = {:{(x+a, x le1),(ax^2 + 1, x ...

Let `f(x) = {:{(x+a, x le1),(ax^2 + 1, x > 1):}`. Show that f is continuous at 1. Find 'a' so that it is derivable at 1.

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Let f(x) = {:{(x+a, x le1),(ax^2 + 1, x > 1):}. Show that f is continu...

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  2. Examine the continuity of f(x) = {:{((x^2-9)/(x-3), x ne 3),(6,x=3):} ...

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  3. If f(X) = (x^2-1)/(x-1 for x ne 1 and f(x) = 2 when x = 1. Show that ...

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  4. The value of the constant k so that the function f(x)={((x^(2)-3x+2)/...

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  5. The constant k, so that the f(x) = {{:((x^(2) - 2x - 3)/(x + 1),"if",x...

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  6. Examine the function f(X) = {:{((1-cos3x)/(x), x ne 0),(0,x=0):} for c...

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  7. For what value of k, function f (x) is continuous at x = 0 where f(x) ...

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  8. A function f(x) is defined as f(x) = {:{((x^2-x-6)/(x-3), x ne 3),(5,x...

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  9. Discuss the continuity of the function f(x), where f(x)= {:{(2-x, x < ...

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  10. Discuss the continuity of the function f(x) at x = 0 , where f(x) ={:{...

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  11. Discuss the continuity of the function f(x) at x = 2, where f(x) = {:{...

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  12. Discuss continuity of f(X) = {:{(-1,x<0),(2-x,xge0):} at x = 0

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  13. Examine the following functions for continuity: f(x) = {:{((2x^2-3x-...

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  14. Examine the following functions for continuity: f(x) = {:{(x+a,x<1),...

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  15. Examine the following functions for continuity: f(x) = {:{((|x-3|)/(...

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  16. Examine the following functions for continuity: f(x) = {:{((x-|x|)/x...

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  17. Examine the following functions for continuity: f(x) = {:{((x^2/2), ...

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  18. Examine the following functions for continuity: f(x) = |x| + |x-1| ...

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  19. Examine the continuity of the function f(x) = {:{(3x-2,xle0),(x+1,x>0)...

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  20. Is the function f(X) = {:{((1-x^n)/(1-x), x ne 1),(n-1,x=1):}, n in N ...

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  21. If f(x) = {{:((x)/(|x| + 2x^2)"," ,x != 0),(k",", x = 0):} Prove tha...

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