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Examine the continuity of the function f...

Examine the continuity of the function `f(x) = 2x^(2) - 1 "at" x = 3 `

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To examine the continuity of the function \( f(x) = 2x^2 - 1 \) at \( x = 3 \), we will follow these steps: ### Step 1: Find \( f(3) \) We first need to evaluate the function at the point \( x = 3 \). \[ f(3) = 2(3^2) - 1 = 2(9) - 1 = 18 - 1 = 17 \] ...
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NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5.1
  1. Prove that the function f(x) = 5x-3is continuous at x = 0, at x =-3and...

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  2. Examine the continuity of the function f(x) = 2x^(2) - 1 "at" x = 3

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  3. Examine the following functions for continuity.(a) f(x)=x-5 (b) f(x)=...

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  4. Prove that the function f(x)=x^nis continuous at x = n, where n is a ...

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  5. Is the function f defined by f(x)={{:(x, if x le 1),(5, if x gt 1):...

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  6. f(x)=2x+3 if x<= 2 and f(x)=2x-3 if x > 2

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  7. f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3)...

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  8. {{:((|x|)/(x)","if x ne 0 ),(0"," if x = 0 ):}

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  9. {{:((x)/(|x|)","if x lt 0 ),(-1"," if x ge 0 ):}

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  10. f(x) {{:(x + 1"," if x ge 1 ),(x^(2)+ 1"," if x lt 1):}

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  11. f(x){{:(x^(3) - 3"," if x le 2 ),(x^(2) + 1"," if x gt 2 ):}

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  12. f(x){{:(10^(3) - 1"," if x le 1 ),(x^(2) "," if x gt 1 ):}

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  13. Is the function defined by f(x)={x+5, ifxlt=1x-5, ifx >1 a continuous...

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  14. Discuss the continuity of the function f, where f is defined by f(x){{...

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  15. f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}

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  16. f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

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  17. Find the relationship between a and b so that the function f defined ...

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  18. For what value of lambdais the function defined by f(x)={lambda(x^2-2...

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  19. Show that the function defined by g(x)=x-[x] is discontinuous at all i...

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  20. Is the function defined by f(x)=x^2-sinx+5continuous at x=pi?

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