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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):}`, f(x) is continuous at x = 0, then k 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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  2. Consider f(x) = {{:((8^(x) - 4^(x) - 2^(x) + 1)/(x^(2))",",x gt 0),(e^...

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  3. Let f(x) = {{:((a(1-x sin x)+b cos x + 5)/(x^(2))",",x lt 0),(3",",x =...

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  4. f(x)={{:(cos^(-1)(cotx),x lt pi/2), (pi[x]-1,x gt pi/2):} where [dot]...

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  5. Let f:[0,1]to[0,1] be a continuous function. Then prove that f(x)=x fo...

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  6. If f(x) = (x + 1)/(x-1) and g(x) = (1)/(x-2), then (fog)(x) is discont...

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  7. Let y(n)(x) = x^(2) + (x^(2))/(1+x^(2))+(x^(2))/((1+x^(2))^(2))+.........

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  8. If g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0 ((2a)^x-xlog(2a)-1)/(x^2), x...

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  9. Find dy/dx if y=(pi)/2-sinx

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  10. Find dy/dx if y= sin2x - x^3

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  11. Let f(x)={1/(|x|)\ \ \ \ \ for\ |x|geq1....a x^2+b\ \ \ \ \ \ \ \ for\...

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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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  16. Find dy/dx if y= x sinx

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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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  20. If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x), then f(x) is, (given f(...

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