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Evalute lim(xrarr0)(ax+ x cosx)/(b sin...

Evalute
`lim_(xrarr0)(ax+ x cosx)/(b sin x)`

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`lim_(x rarr 0) (ax+x cos x)/(b sin x)=lim_(x rarr0)[(x(a+cos x))/(b sin x)]= (lim_(x rarr 0) (a + cos x))/(b lim_(x rarr 0) (sin x)/x)=(a+1)/(b+1) = (a+1)/b`
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V PUBLICATION-LIMITS AND DERIVATIVES-QUESTION BANK
  1. Evaluate the following limits lim(x rarr 0) (cos x)/(pi-x)

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  2. Evaulate underset (x rarr 0)Lim (cos 2x-1)/(cos x-1).

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  3. Evalute lim(xrarr0)(ax+ x cosx)/(b sin x)

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  4. Evaluate lim(x rarr 0) x sec x

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  5. Evaluate lim(x rarr 0) (sin ax + bx )/(ax + sin bx) , a, b, a + b ne 0

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  6. Evaluate underset (x rarr 0)lim(cosec x-cot x)

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  7. Evalute lim(xrarrpi/2)(tan2x)/(x-pi/2)

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  8. Find lim(xrarr0) f(x) and lim(xrarr1) f(x) where f(x)={(2x+3,xle0), ...

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  9. Find lim(xrarr1) f(x) where f(x)={(x^2-1,xle1), (-x^2-1,x>1):}

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  10. Evalute lim(xrarr0)f(x) , where f(x)={(absx/x, x ne 0),(0,x=0):}

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  11. Evalute lim(xrarr0)f(x) , where f(x)={(absx/x, x ne 0),(0,x=0):}

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  12. Find lim(x rarr 5) f(x), where f(x) = |x| -5

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  13. If f(x)={(a+bx,x<1),(4,x=1),(b-ax,x>1):} and lim(xrarr1)f(x)=f(1) , ...

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  14. Let a(1), a(2), …………….,a(n) be fixed real numbers and define a functio...

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  15. If f(x)={(absx + 1 , x lt 0),(0 , x = 0),(absx - 1 , x gt 0) :} , for ...

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  16. If the function f(x) satisfies lim(x rarr 1) (f(x)-2)/(x^(2)-1) = pi, ...

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  17. Find the derivative at x = 2 of the function f(x) = 3x.

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  18. Find the derivative of the function f(x)=2x^2+3x-5 at x=-1.Also prove ...

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  19. Find the derivative of sin x at x = 0.

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  20. Find the derivative of f(x) = 3 at x = 0 and x =3.

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