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Write the value of lim(x->a)(xf(a)-af(x)...

Write the value of `lim_(x->a)(xf(a)-af(x))/(x-a)`.

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To solve the limit \( \lim_{x \to a} \frac{xf(a) - af(x)}{x - a} \), we will follow a systematic approach using the definition of derivatives. ### Step-by-Step Solution: 1. **Rewrite the Limit**: We start with the limit expression: \[ L = \lim_{x \to a} \frac{xf(a) - af(x)}{x - a} ...
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RD SHARMA-DERIVATIVES-Solved Examples And Exercises
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  2. Write the value of lim(x->c)(f(x)-f(c))/(x-c).

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  3. Write the value of lim(x->a)(xf(a)-af(x))/(x-a).

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  4. If x<2, then write the value of d/(dx)(sqrt(x^2-4x+4))dot

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  5. If pi/2 lt x lt pi, then find d/dx(sqrt((1+cos2x)/2))

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  6. Write the value of d/(dx)(x \ |x|).

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  7. Write the value of d/(dx){(x+|x|)|x|}dot

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  8. If f(x)=|x|+|x-1| , write the value of d/(dx)(f(x)).

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  9. Write the value of the derivative of f(x)=|x-1|+|x-3| \ at \ x = 2.

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  10. If f(x)=(x^2)/(|x|), write d/(dx)(f(x))

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  11. Write the value of d/(dx)(log|x|).

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  12. If f(1)=1,f^(prime)(1)=2, then write the value of lim(x->1)(sqrt(f(x))...

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  13. Write the derivative of f(x)=3 \ |2+x| at x=-3.

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  14. If |x|<1 and y=1+x+x^2+x^3+... , then write the value of (dy)/(dx)dot

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  15. Let f(x)=x-[x], x in RR, then f^(prime)(1/2) is a. 3/2 b. 1 c. 0 d. -1

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  16. If f(x)=(x-4)/(2sqrt(x)), then f^(prime)(1) is a. 5/4 b. 4/5 c. 1 d. 0

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  17. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+... , then (dy)/(dx)= a. y+1 b. y-...

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  18. If f(x)=1-x+x^2-x^3+...-x^(99)+x^(100), then f^(prime)(1) equals a. 15...

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  19. If y=(1+1/(x^2))/(1-1/(x^2)), then (dy)/(dx)= a. -(4x)/((x^2-1)^2) b. ...

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  20. If y=sqrt(x)+1/(sqrt(x)), then (dy)/(dx) \ at \ x=1 is a. 1 b. 1/2 c....

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