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If f(x)=1-x^2-x^3+......-x^(99)+x^(100) ...

If `f(x)=1-x^2-x^3+......-x^(99)+x^(100)` then `f^(prime)(1)` equals

A

150

B

`-50`

C

`-150`

D

50

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x) =1-x+x^(2)-x^(3)+………..-x^(99)+x^(100)`
`f^(')(x) = 0-1+2x-3x^(2)+…..-99x^(98)+100x^(99)`
`=-1+2x-3x^(2)+…..-99x^(98)+100x^(99)`
`therefore f^(')(1)=-1+2-3+…..-99+100`
`=(-1 -3-5 -…….-99) + (2+4+……+100)` `[therefore S_(n) = n/2{2a+(n-1)d}]`
`=-50/2[2xx1+(50-1)2]+50/2[2 xx 2+(50-1)2]`
`=-25[2+49xx2]+54[4+49xx2]`
`=-25 xx 100 + 25 xx 102`
`=-2500 +2550`
=50
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NCERT EXEMPLAR-LIMITS AND DERIVATIVES -OBJECTIVE TYPE QUESTIONS
  1. lim(xrarr1)(x^(m)-1)/(x^(n)-1) is equal to

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  2. lim(thetato0)(1-cos4theta)/(1-cos6theta) is equal to

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  3. lim(xrarr0)("cosec"x-cotx)/(x) is equal to

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  4. lim(xrarr0)(sinx)/(sqrt(x+1)-sqrt(1-x)) is equal to

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  5. lim(xrarr(pi//4))(sec^2x-2)/(tanx-1) is

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  6. lim(x->1)[(2x-3)(sqrtx-1)]/[2x^2+x-3]

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  7. If f(x) = { sin[x] /[x],[x] != 0 ; 0, [x] = 0} , Where[.] denotes the ...

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  8. lim(xrarr0)(|sinx|)/(x) is equal to

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  9. If f(x) ={x^2-1, 0 lt x lt 2 , 2x+3 , 2 le x lt 3then the quadratic eq...

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  10. lim(xrarr0)(tan2x-x)/(3x-sinx) is equal to

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  11. if f(x) =x-[x], in R, then f^(')(1/2) is equal to

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  12. if y=sqrt(x) + 1/sqrt(x), then (dy)/(dx) at x=1 is equal to

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  13. If f(x) =(x-4)/(2sqrt(x)), then f^(')(1) is equal to

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  14. if y=(1+1/x^(2))/(1-1/(x)^(2)),then (dy)/(dx) is equal to

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  15. if y=(sinx+cosx)/(sinx-cosx), then (dy)/(dx) at x=0 is equal to

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  16. if y=(sin(x+9))/(cosx), then (dy)/(dx) at x=0 is equal to

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  17. If f(x)=1+x+(x^2)/2++(x^(100))/(100), then f^(prime)(1) is equal to

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  18. Find the derivative of (x^(n)-a^(n))/(x-a) for some constant a.

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  19. If f(x)=x^(100)+x^(99)++x+1, then f^(prime)(1) is equal to

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  20. If f(x)=1-x^2-x^3+......-x^(99)+x^(100) then f^(prime)(1) equals

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