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Continuity of Functions (Grades 11-12)

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Continuity of Functions

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