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If f(x)={(x-absx,x<2),(0,x=2),(3x-5,x>2)...

If `f(x)={(x-absx,x<2),(0,x=2),(3x-5,x>2):}`
Find `lim_(xrarr2)f(x)`

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MAXIMUM PUBLICATION-CONTINUITY & DIFFERENTIABILITY-EXAMPLE
  1. Evalute lim(xrarr0)frac(kcosx)(pi-2x) (Hint: Put pi-2x=y , where k i...

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  2. Find the value of k if f(x) is a continious function give by f(x)={(...

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  3. If f(x)={(x-absx,x<2),(0,x=2),(3x-5,x>2):} Find lim(xrarr2)f(x)

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  4. Is f(x) =x^2continuous at x=2 ?

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  5. If x=2costheta , y=3sintheta Find dy/dx .

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  6. If x=2costheta , y=3sintheta Find (d^2y)/(dx^2) .

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  7. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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  8. Find dy/dx If y=sin^(-1)(frac(1-x^2)(1+x^2)) , 0 < x < 1

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  9. Let f(x)={(cosx,0lexlec),(sinx,c<xlepi)} Find the value of c if f is...

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  10. Find dy/dx if x=2sintheta , y=3costheta

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  11. Examine whether the function defined by f(x)={(x+5,xle1),(x-5,x>1):}...

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  12. If x=a^(sin^(-1)t) , y=a^(cos^(-1)t) , a>0 , show that dy/dx=-y/x

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  13. If f(x)={(1-x,0<x<1),{(1+x,1<x<2):} then which of the following is not...

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  14. If (1, xle 3), (ax+b, 3<x<5),(7,5lex) find f(3^+) and f(3^-)

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  15. If {(1,xle3), (ax+b,3<x<5) ,(7,5lex):} hence find the value of 'a' a...

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  16. Consider f(x)={(2x+3,xle2),(x+2k,x>2):} Find f(2)

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  17. Consider f(x)={(2x+3,xle2),(x+2k,x>2):} Evalute lim(xrarr2^+)f(x)

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  18. Consider f(x)={(2x+3,xle2),(x+2k,x>2):} Find the value of k, if is c...

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  19. Find dy/dx if y=(logx)^cosx

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  20. Find dy/dx of x=2at^2 , y=at^4

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