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If the function defined by : f(x) = {:...

If the function defined by :
`f(x) = {:{(2x-1,x<2),(a,x=2),(x+1,x>2):}` is continuous at x =2, find the value of 'a'. Also discuss the continuity of f(x) at x =3.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. In the following, determine the constant so that given function is con...

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  2. For what value of 'k' is the function defined by f(x) = {:{(k(x^2+2),i...

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  3. If the function defined by : f(x) = {:{(2x-1,x<2),(a,x=2),(x+1,x>2):...

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  4. If the following function f(x) is continuous at x = 0, find the value ...

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  5. Determine the constants 'a' and 'b' so that the function 'f' defined b...

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  6. Determine the constants 'a' and 'b' so that the function 'f' defined b...

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  7. If the function f(x) given by: f(x) = {:{(2ax+b,ifx>1),(9,ifx=1),(6a...

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  8. Find the values of a and b so that the following function is continuou...

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  9. Find 'a' and 'b' if the function: f(x) = {:{((sinx)/x, -2lex<0),(a.2...

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  10. Find the values of 'p' and 'q' for which: f(x) = {:{((1-sin^3x)/(3co...

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

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  12. A man is driving a car on the dangerous path given by: f(x) = {:{((1...

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  13. Find all the points of discontinuity of the function f defined by f(x)...

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  14. Find all points of discontinuity of f, where f is defined by : f(x)={(...

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  15. Find all the points of discontinuity of f, where f is defined by f(x...

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  16. Show that the following functions are continuous: f(x) = sin(x^2)

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  17. Show that the following functions are continuous: f(x) = cos(x^2)

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  18. Show that the following functions are continuous: f(x) = |cosx|

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  19. Show that the function 'f' given by: f(x) = |x| + |x-1|, x in R is c...

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  20. Show that the function 'f' given by: f(x) = |x-1|+|x-2|, x in R is c...

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