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Continuity of Functions (Grades 11-12)

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Continuity of Functions

1. 
If [math]lim_(x->5)f(x)[/math] exists, then [math]f(5)[/math] must exist.
  1. True
  2. False
2. 
If [math]lim_(x->2)f(x)=L[/math], then [math]L=f(2).[/math]
  1. True
  2. False
3. 
If [math]f(x)[/math] is continuous at [math]x = 3[/math], then [math]lim_(x->3)f(x)=f(3).[/math]
  1. True
  2. False
4. 
If f(x) is continuous at x = 5, then f'(5) must exist.
  1. True
  2. False
5. 
Is [math]h(x)=(x-4)/(x^2-5x+4)[/math] continuous or discontinuous at x = 1? Justify using continuity test. If discontinuous, what type?
  1. Continuous
  2. Infinite discontinuity
  3. Jump discontinuity
  4. Removable discontinuity
6. 
Is [math]h(x)=(x-4)/(x^2-5x+4)[/math] continuous or discontinuous at x = 3? Justify using continuity test. If discontinuous, what type?
  1. Continuous
  2. Infinite discontinuity
  3. Jump discontinuity
  4. Removable discontinuity
7. 
Is the following function continuous at [math]x=3 ?[/math] If it is not, then choose the appropriate type of discontinuity. [math] \ f(x) = (x^2 - x - 6)/(x^2 - 3x)[/math]
  1. Continuous
  2. Infinite discontinuity
  3. Removable discontinuity
  4. Jump discontinuity
8. 
If [math] f(x) = {{:( (log(1 - 2x) \ - \ log(1 - 3x))/x, x!=0),(a \ \ \ \ \ \ \ \ \ \ \ \ \ , x=0):} [/math] is continuous at [math] x=0 [/math], then [math] a=[/math]
  1. 5
  2. 1
  3. -1
  4. 6
9. 
If the function [math] f(x)= {{:( (3sinx-sin3x )/x^3, x!=0), (a \ \ \ \ \ \ \ \ , x=0):} [/math] is continuous at [math]x=0[/math], then what is the value of [math]a[/math]?
  1. -4
  2. 4
  3. 0
  4. 6
10. 
If [math] f(x) = { {:(sin(4x)/(5x) + a, x>0), (6x+4-b, x<=0):}[/math] is continuous at [math]x=0[/math], then [math]a+b=[/math]
  1. [math]1/5[/math]
  2. [math]3[/math]
  3. [math]-14/5[/math]
  4. [math]16/5[/math]
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