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Limits, Continuity and Differentiability

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  1. 201.Let S be the set of all points in (-,) at which the function f(x)= x, x is not differentia…
  2. 202.For x>1, if (2x)^2y=4e^2x-2y, then (1+_e2x)^2dydx is equal to:
  3. 203.Let f:RR be a function such that f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3), xR.
  4. 204.If x=3 t and y=3 t, then the value of d^2ydx^2 at t=4, is:
  5. 205.If the function f defined on (6,3) by f(x)=cases√2 x-1 x-1, & x4, & x=4cases is continuous…
  6. 206.If f(x)=[x]-[ x4], xR, where [x] denotes the greatest integer function, then:
  7. 207.If the function f(x)=casesa|-x|+1, & x5|x-|+3, & x>5cases is continuous at x=5, then the v…
  8. 208.Let f:[-1,3]R be defined as f(x)=cases|x|+[x], & -1 x<1+|x|, & 1 x<2+[x], & 2 x3cases, whe…
  9. 209.If f(x)=cases(p+1)x+ xx, & x<0, & x=0x+x^2- xx^3/2, & x>0cases is continuous at x=0, then …
  10. 210.Let f(x)=_e( x), (0<x<) and g(x)=^-1(e^-x), (x0).
  11. 211.Let f:RR be differentiable at cR and f(c)=0.
  12. 212.Let f(x)=15-|x-10|, xR.
  13. 213.If f(1)=1, f'(1)=3, then the derivative of f(f(f(x)))+(f(x))^2 at x=1 is:
  14. 214.If e^y+xy=e, the ordered pair (dydx,d^2ydx^2) at x=0 is equal to:
  15. 215.The derivative of ^-1( x- x x+ x), with respect to x2, where x(0,2), is:
  16. 216.If 2y=^-1(√3 x+ x x-√3 x)^2, x(0,2), then dydx is equal to:
  17. 217.If the function f defined as f(x)=1x-k-1e^2x-1, x0, is continuous at x=0, then the ordered…
  18. 218.Let f(x)=cases(x-1)^12-x, & x>1, x2, & x=2cases.
  19. 219.Let S=tR:f(x)=|x-|(e^|x|-1)|x| is not differentiable at t.
  20. 220.If x=2^^-1t and y=2^^-1t (|t|1), then dydx is equal to.
  21. 221.If f(x)=vmatrix x & x & 12 x & x^2 & 2x x & x & 1vmatrix, then _x0f'(x)x
  22. 222.If f(x)=^-1(23^x1+9^x), then f'(-12) equals.
  23. 223.If x^2+y^2+ y=4, then the value of d^2ydx^2 at the point (-2,0) is
  24. 224.The value of k for which the function f(x)=cases454x5x, & 0<x<2+25, & x=2cases is continuo…
  25. 225.If for x(0,14), the derivative of ^-1(6x x1-9x^3) is x g(x), then g(x) equals:
  26. 226.If y^1/5+y^-1/5=2x and (x^2-1)d^2ydx^2+ xdydx+ky=0, then +k is equal to
  27. 227.Let f be a polynomial function such that f(3x)=f'(x)f''(x), for all xR.
  28. 228.If y=(x+x^2-1)^15+(x-x^2-1)^15, then (x^2-1)d^2ydx^2+xdydx is equal to
  29. 229.Let a,bR (a0).
  30. 230.If the function f(x)=cases-x, & x<1+^-1(x+b), & 1 x2cases is differentiable at x=1, then a…
  31. 231.For xR, f(x)=|2- x| and g(x)=f(f(x)), then
  32. 232.Let k be a non-zero real number.
  33. 233.If the function g(x)=caseskx+1, & 0 x3+2, & 3<x5cases is differentiable, then the value of…
  34. 234.If Rolle's theorem holds for the function f(x)=2x^3+bx^2+cx, x[-1,1], at the point x=12, t…
  35. 235.If the function f(x)=cases√2+ x-1(-x)^2, & x, & x=cases is continuous at x=, then k equals…
  36. 236.If f(x) is continuous and f(92)=29, then _x0f(1-3xx^2) is equal to:
  37. 237.Let f:RR be a function such that |f(x)| x^2 for all xR.
  38. 238.Let f,g:RR be defined by f(x)=casesx1x, & x00, & x=0cases, and g(x)=xf(x).
  39. 239.If f(x)=x^2-x+5, x>12, and g(x) is its inverse function, then g'(7) equals:
  40. 240.If f and g are differentiable functions in [0,1] satisfying f(0)=2=g(1), g(0)=0 and f(1)=6…
  41. 241.Let f(x)=x|x|, g(x)= x, and h(x)=(g f)(x).
  42. 242.Let for i=1,2,3, p_i(x) be a polynomial of degree 2 in x; p_i'(x) and p_i''(x) be the firs…
  43. 243.If the Rolle's theorem holds for the function f(x)=2x^3+ax^2+bx in the interval [-1,1] for…
  44. 244.Consider the function f(x)=[x]+|1-x|, -1 x3, where [x] is the greatest integer function.
  45. 245.Let f be a composite function of x defined by f(u)=1u^2+u-2, u(x)=1x-1.
  46. 246.Let f(x)=-1+|x-2| and g(x)=1-|x|; then the set of all points where f g is discontinuous is…
  47. 247.If y=(^-1x), then dydx at x=1 is equal to:
  48. 248.If the curves x^2+y^24=1 and y^3=16x intersect at right angles, then a value of is:
  49. 249.For a>0, t(0,2), let x=a^^-1t and y=a^^-1t.
  50. 250.Let f(x)=x^2-xx^2+2x, x0,-2.