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If f(x + y) = f(x)f(y) for all x, y and ...

If f(x + y) = f(x)f(y) for all x, y and and f(x) = 1 + x g(x), where `lim_(xrarr0)g(x)=1`) , show that f'(x) = f(x).

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UNITED BOOK HOUSE-SETS,FUNCTIONS AND CALCULUS-EXERCISE
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  2. Find the inverse of the function f(x)=(x^4+x^2+1)/x^2

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  3. If f(x)=cos[pi^2]x+cos[-pi^2]xwhere [x] denotes the greatest integer f...

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  4. Evaluate the following limits : lim(xrarrpi/2)(xtanx-pi/2secx)

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  5. Evaluate lim(xrarrpi//4)(4sqrt2-(cosx+sinx)^5)/(1-sin2x)

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  6. Evaluate :lim(xrarr0)((a+x)^2sin(a+x)-a^2sina)/pi

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  7. Evaluate the following limits :lim(xrarr0)(xtan2x-2xtanx)/((1-cos2x)^2...

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  8. Let f(x)=4^x/(4^x+2)prove.that f(x) + f(1- x)= 1. Hence prove that f(1...

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  9. If f(a) = 2, f'(a) = 1, g(a) = -1 and g'(a) = 2, find the value of lim...

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  10. If f(x + y) = f(x)f(y) for all x, y and and f(x) = 1 + x g(x), where ...

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  11. Find the domain of definition of the function y(x) given by the equati...

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  12. If f(x+1/x)=x^2+1/x^2,find f(x).

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  13. If phi(x)is the inverse of g(x)and g'(x)=1/(1+x^3),show that phi'(x)=1...

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  14. Differentiate tan^-1((sqrt(1+x^2)-1)/x)with respect to tan^-1 x

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  15. If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y),show that dy/dx=sqrt((1-y^2)/(1-x^2)...

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  16. If y=sqrt((a-x)(x-b))-(a-b)tan^-1sqrt((a-x)/(x-b)),show that dy/dx=sqr...

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  17. If y=y=sqrtx^(sqrtx^(sqrtx^(...oo)),show that xdy/dx=y^2/(2-ylogx)

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  18. The value of tanalpha+2tan(2alpha)+4tan(4alpha)+...+2^(n-1)tan(2^(n-1)...

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