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Consider f(x) = {{:((8^(x) - 4^(x) - 2^(...

Consider `f(x) = {{:((8^(x) - 4^(x) - 2^(x) + 1)/(x^(2))",",x gt 0),(e^(x)sin x + pi x + k log 4",",x lt 0):}` Then, f(0) so that f(x) is continuous at x = 0, is

A

log 4

B

log 2

C

(log 4) (log 2)

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
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  12. If f(x) = {{:(A+Bx^(2)",",x lt 1),(3Ax - B+2",",x ge 1):}, then A and ...

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  13. If f(x) = {{:(|x-1|([x]-x)",",x ne 1),(0",",x = 1):}, then

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  14. If f(x) = {{:([cos pi x]",",x le 1),(2{x}-1",",x gt 1):}, where [.] an...

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  15. If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):}, then g(x)...

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  17. Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for...

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  18. Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists an...

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  19. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

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