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If y=1+x+(x^(2))/(2!)+(x^(2))/(3!)+……+(x...

If `y=1+x+(x^(2))/(2!)+(x^(2))/(3!)+……+(x^(n))/(n!)` then `(dy)/(dx)`=…………

A

y

B

y-x

C

`y-(x^(n))/(n!)`

D

`y-(x^(n))/((n-1)!)`

Text Solution

Verified by Experts

The correct Answer is:
C
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KUMAR PRAKASHAN-LIMITS AND DERIVATIVES-Textbook based MCQs
  1. lim(xtoa)(x^((1)/(3))-a^((1)/(3)))/(x^((1)/(5))-a^((1)/(5))),(agt0)=……...

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  2. If 5f (x)+3f ((1)/(x))=x+2,y=xf(x),then the value of ((dy)/(dx))(x=1) ...

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  3. If y=1+x+(x^(2))/(2!)+(x^(2))/(3!)+……+(x^(n))/(n!) then (dy)/(dx)=…………

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  4. lim(xrarra)(xf(a)-af(x))/(x-a)=f(a)-(a)f'(a).

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  5. If f(x)=x^(n-1)+x^(n-2)+….+1,-1ltxlt1 then f'(x)=…….

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  6. If f(4)=16 ,f'(4)=2 and f is differentiable of x=4 then lim(xto4)(sqrt...

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  7. (d)/(dx)(x+|x|)|x|=……..(xlt0)

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  8. (d)/(dx)(sin180^(@))=………

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  9. (d)/(dx)(sinx^(@))=…….

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  10. (d)/(dx)(sqrt(sinx))=………..(0ltxlt (pi)/(2))

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  11. (d)/(dx)(tan^(2)x)=……..

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  12. (d)/(dx)sqrt(x^(2)-2x+1)=………

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  13. lim(yto0^(+))(3sqrt(y)+3sqrt(y^(2))-4sqrt(y^(3)))/(3sqrt(y)+y +4sqrt(y...

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  14. lim(xto1)(x^(365)-365x+364)/((x-1)^(2)) =………..

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  15. If lim(yto-2)(3x^(2)ax+a+3)/(x^(2)+x-2) limit exists then a=………..

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  16. lim(hto0)(4sqrt(x+h)-4sqrt(x))/(h)=………...

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  17. lim(xto1)(x+x^(2)+x^(3)+…….+n^(n)-n)/(x-1)=……….,where nin N

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  18. f(x)={{:((1-sinx)/(pi-2x)","xne(pi)/(2)),(lambda ","" "x=(pi)/(2))...

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  19. lim(xtoa)(f(x)-f(a))/(x^(3)-a^(3))=……………

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  20. If (d)/(dx)((1+x^(4)+x^8)/(1+x^(2)+x^(4)))=ax^(3)+bx then …………….

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