11th Maths Weekly Test-2 ( Differential Calculus - Limits and Continuity )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-2 ( Differential Calculus - Limits and Continuity )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Complete the table using calculator and use the result to estimate the limit.
\(\underset{x\rightarrow{-3}}{lim}{\sqrt{1-x}-2\over x+3}\)

x -3.1 -3.01 -3.00 -2.999 -2.99 -2.9

f(x) 0.24845 -0.24984 -0.24998 -0.25001 -0.25015 -0.25158

Find \(\underset { x\rightarrow 1 }{ lim } \) fix), if \(f(x)=\{ \begin{matrix} { x }^{ 2 }-1 & x\le 1 \\ -{ x }^{ 2 }-1 & x>1 \end{matrix}\)

Consider the function f(x) = \(\sqrt{x},x\ge0.\)
Does\(lim_{x\rightarrow0}f(x)\) exist?

Evaluate \(\underset{ x\rightarrow a }{lim}{ \frac { \sqrt { x } +\sqrt { a } }{ x+a } } \)

Evaluate the following limits :\(\underset{x\rightarrow 0}{lim}{sin (a+x)-sin(a-x)\over x}\)

Evaluate the following limits :\(\underset{x\rightarrow 0}{lim}{tan 2 x\over sin 5 x}\)

Find the positive integer n so that \(lim_{x\rightarrow 3}{x^n-3^n\over x-3}=27\)

Find the points of discontinuity of the function f, where f(x)=\(\begin{cases} 4x+5, & if\quad x\le 3 \\ 4x-5, & if\quad x>3 \end{cases}\)

Evaluate \(lim_{x\rightarrow 2^-}\left\lfloor x \right\rfloor \) and \(lim_{x\rightarrow 2^+}\left\lfloor x \right\rfloor \) .

Compute \(lim_{x\rightarrow8}(5x)\)

Part - B

Generic 5 - Answer All Question

Evaluate the following limits :\(\underset{x\rightarrow0}{lim}{e^x-e^{-x}\over sin x}\)

Which of the following functions f has a removable discontinuity at x = x₀? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R
\(f(x)={3-\sqrt{x}\over 9-x},x_o=9\)

If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2?

Evaluate the following limits :
\(\underset{x\rightarrow0}{lim}{\sqrt{1-x}-1\over x^2}\)

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x	-3.1	-3.01	-3.00	-2.999	-2.99	-2.9
f(x)	0.24845	-0.24984	-0.24998	-0.25001	-0.25015	-0.25158

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11th Maths Weekly Test-2 ( Differential Calculus - Limits and Continuity )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-2 ( Differential Calculus - Limits and Continuity )-Aug 2020

Part - A

Generic 2 - Answer All Question

Complete the table using calculator and use the result to estimate the limit. \(\underset{x\rightarrow{-3}}{lim}{\sqrt{1-x}-2\over x+3}\) x -3.1 -3.01 -3.00 -2.999 -2.99 -2.9 f(x) 0.24845 -0.24984 -0.24998 -0.25001 -0.25015 -0.25158

Find \(\underset { x\rightarrow 1 }{ lim } \) fix), if \(f(x)=\{ \begin{matrix} { x }^{ 2 }-1 & x\le 1 \\ -{ x }^{ 2 }-1 & x>1 \end{matrix}\)

Consider the function f(x) = \(\sqrt{x},x\ge0.\) Does\(lim_{x\rightarrow0}f(x)\) exist?

Evaluate \(\underset{ x\rightarrow a }{lim}{ \frac { \sqrt { x } +\sqrt { a } }{ x+a } } \)

Evaluate the following limits :\(\underset{x\rightarrow 0}{lim}{sin (a+x)-sin(a-x)\over x}\)

Evaluate the following limits :\(\underset{x\rightarrow 0}{lim}{tan 2 x\over sin 5 x}\)

Find the positive integer n so that \(lim_{x\rightarrow 3}{x^n-3^n\over x-3}=27\)

Find the points of discontinuity of the function f, where f(x)=\(\begin{cases} 4x+5, & if\quad x\le 3 \\ 4x-5, & if\quad x>3 \end{cases}\)

Evaluate \(lim_{x\rightarrow 2^-}\left\lfloor x \right\rfloor \) and \(lim_{x\rightarrow 2^+}\left\lfloor x \right\rfloor \) .

Compute \(lim_{x\rightarrow8}(5x)\)

Part - B

Generic 5 - Answer All Question

Evaluate the following limits :\(\underset{x\rightarrow0}{lim}{e^x-e^{-x}\over sin x}\)

Which of the following functions f has a removable discontinuity at x = x0? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R \(f(x)={3-\sqrt{x}\over 9-x},x_o=9\)

If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2?

Evaluate the following limits : \(\underset{x\rightarrow0}{lim}{\sqrt{1-x}-1\over x^2}\)

Comment

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Complete the table using calculator and use the result to estimate the limit.
\(\underset{x\rightarrow{-3}}{lim}{\sqrt{1-x}-2\over x+3}\)

x -3.1 -3.01 -3.00 -2.999 -2.99 -2.9

f(x) 0.24845 -0.24984 -0.24998 -0.25001 -0.25015 -0.25158

Consider the function f(x) = \(\sqrt{x},x\ge0.\)
Does\(lim_{x\rightarrow0}f(x)\) exist?

Which of the following functions f has a removable discontinuity at x = x₀? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R
\(f(x)={3-\sqrt{x}\over 9-x},x_o=9\)

Evaluate the following limits :
\(\underset{x\rightarrow0}{lim}{\sqrt{1-x}-1\over x^2}\)