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.
- True
- False
2.
If [math]lim_(x->2)f(x)=L[/math], then [math]L=f(2).[/math]
- True
- False
3.
If [math]f(x)[/math] is continuous at [math]x = 3[/math], then [math]lim_(x->3)f(x)=f(3).[/math]
- True
- False
4.
If f(x) is continuous at x = 5, then f'(5) must exist.
- True
- 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?
- Continuous
- Infinite discontinuity
- Jump discontinuity
- 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?
- Continuous
- Infinite discontinuity
- Jump discontinuity
- 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]
- Continuous
- Infinite discontinuity
- Removable discontinuity
- 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]
- 5
- 1
- -1
- 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]?
- -4
- 4
- 0
- 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]
- [math]1/5[/math]
- [math]3[/math]
- [math]-14/5[/math]
- [math]16/5[/math]
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