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Differentiability Maths - Differentiability

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 63 questions in this chapter.

Question types

Differentiability question types

63 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

63
Questions
4
Question groups
5
Question types
Sample Questions

Differentiability questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
If f(x) = |3 − x| + (3 + x), where (x) denotes the least integer greater than or equal to x, then f(x) is:
  1. Continuous and differentiable at x = 3
  2. Continuous but not differentiable at x = 3
  3. Differentiable nut not continuous at x = 3
  4. Neither differentiable nor continuous at x = 3
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Q 2M.C.Q (1 Marks)1 Mark
If $\text{f(x)}=\text{a}|\sin\text{x}|+\text{be}^{|\text{x}|}+\text{c|x|}^3$and if f(x) is differentiable at x = 0, then:
  1. $\text{a}=\text{b}=\text{c}=0$
  2. $\text{a}=0,\text{b}=0;\text{c}\in\text{R}$
  3. $\text{b}=\text{c}=0,\text{a}\in\text{R}$
  4. $\text{c}=0,\text{a}=0,\text{b}\in\text{R}$
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Q 3M.C.Q (1 Marks)1 Mark
The set points where the function f(x) given by $\text{f(x)=}|\text{x}-3|\cos\text{x}$ is  diffrentiable, is:
  1. R
  2. R - {3}
  3. $(0,\infty)$
  4. None of these.
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Q 4M.C.Q (1 Marks)1 Mark
If $\text{f(x)}=\begin{cases}\frac{1-\cos\text{x}}{\text{x}\sin\text{x}}, & \text{x}\neq 0\\\frac{1}{2} & \text{x}= 0\end{cases}$ then at x = 0, f(x) is:
  1. Continuous and differentiable.
  2. Differentiable but not continuous.
  3. Continuous but not differentiable.
  4. Neither continuous not differentiale.
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Q 5M.C.Q (1 Marks)1 Mark
The function$\text{f(x)}=1+|\cos\text{x}|$ is:
  1. Continuous no where.
  2. Continuous everywhere.
  3. Not differentiable at x = 0
  4. Not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}.$
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Q 102 Marks2 Marks
If f(x) is differentiable at x = c, then write the value of $\text{f}\lim_\limits{\text{x}\rightarrow{\text{c}}}\text{f(x)}.$
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Q 153 Marks3 Marks
Examine the differentialiblilty of the function f defined by $\text{f(x)}=\begin{cases}2\text{x}+3 & \text{if}-3\leq\text{x}\leq-2\\\text{x}+1 & \text{if} -2\leq\text{x}\leq0\\\text{x}+2&\text{if}\ 0\leq\text{x}\leq1\end{cases}$
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Q 164 Marks4 Marks
Discuss the continuity and differentiability of,

$\text{f(x)}=\begin{cases}(\text{x}-\text{c})\cos\Big(\frac{1}{\text{x}-\text{c}}\Big), & \text{x}\neq 0\\0, & \text{x}= 0\end{cases}$

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Q 174 Marks4 Marks
Finde the value of a and b, if the function f(x) defined by $\text{f(x)}\begin{cases}\text{x}^2+3\text{x}+\text{a}, &\text{x}\leq1\\\text{bx}+2, & \text{x}>1\end{cases}$is differentiable at x = 1.
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Q 194 Marks4 Marks
If $\text{f(x)}=\begin{cases}\text{ax}^2-\text{b}, & \text{if |x|}<1\\\frac{1}{|\text{x}|}, & \text{if |x|}\geq1\end{cases}$ is differentiable at x = 1, find a, b.
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Q 204 Marks4 Marks
Show that the function $\text{f(x)}\begin{cases}\text{x}^\text{m}\sin(\frac{1}{\text{x}}), &\text{x}\neq0 \\0 ,& \text{x}=0\end{cases}$
Continuous but not diffierentiable at x = 0, if 0 < m < 1
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