Mathematics Questions and Answers – Continuity

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Continuity”.

1. What is the mathematical expression for the definition of continuity?
a) lim_x→c⁡f(x) = f(c) ∀ c ∈ a
b) lim_x→c⁡f(x) = f(c) ∀ c ∈ (a,b)
c) lim_x→c⁡f(x) = f(c) ∀ c ∈ b
d) lim_x→a⁡f(x) = f(c) ∀ c ∈ (a,b)
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2. What is the mathematical expression for f is continuous on (a,b)?
a) lim_x→c⁡f(x) = f(c) ∀ c ∈ a
b) lim_x→c⁡f(x) = f(c) ∀ c ∈ (a,b)
c) lim_x→c⁡f(x) = f(c) ∀ c ∈ b
d) lim_x→a⁡f(x) = f(c) ∀ c ∈ (a,b)
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3. What is the mathematical expression for f is right continuous on (a,b)?
a) lim_x→a+⁡f(x)=f(a)
b) lim_x→a+⁡f(x)=f(b)
c) lim_x→b+⁡f(x)=f(a)
d) lim_x→a-⁡f(x)=f(a)
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4. What is the mathematical expression for f is left continuous on (a,b)?
a) lim_x→a-⁡f(x)=f(a)
b) lim_x→b-⁡f(x)=f(b)
c) lim_x→a+⁡f(x)=f(b)
d) lim_x→b+⁡f(x)=f(b)
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5. f(x) = c ∀ x ∈ R is continuous on R for a fixed c ∈ R.
a) False
b) True
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6. What are the kinds of discontinuity?
a) Minor and major kinds
b) Increment and decrement kinds
c) First and second kinds
d) Zero and one kinds
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7. Is f(x) = \( \begin{cases}
\frac {sin2x}{x} & if \, x \neq 0 \\
1 & if \, x = 0 \\
\end{cases} \) a continuous function?
a) Only in some cases
b) Cannot be determined
c) Continuous
d) Not continuous
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8. What is/are conditions for a function to be continuous on (a,b)?
a) The function is continuous at each point of (a,b)
b) The function is right continuous
c) The function is left continuous
d) Right continuous, left continuous, continuous at each point of (a,b)
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9. lim_x→a+⁡f(x)=f(a) then f(x) is right continuous at x = a.
a) True
b) False
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10. lim_x→a⁡-f(x)=f(b) then f(x) is left continuous at x = a.
a) False
b) True
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Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.