Examine sin |x| is a continuous function. - Mathematics

Question

Examine sin |x| is a continuous function.

Sum

Solution

Let f(x) = sin $| x |$

x = c $\in$ on R

$lim_{x \to c} f (x) = lim_{x \to c} (\sin | x |) = \sin | c |$

f(c) = sin $| c |$

Hence, f is a continuous function on x = c $\in$ R.

shaalaa.com

Algebra of Continuous Functions

Is there an error in this question or solution?

Q 33 Q 32 Q 34

Chapter 5: Continuity and Differentiability - Exercise 5.1 [Page 161]

APPEARS IN

NCERT Mathematics [English] Class 12

Chapter 5 Continuity and Differentiability
Exercise 5.1 | Q 33 | Page 161

Video TutorialsVIEW ALL [3]

view
Video Tutorials For All Subjects
Algebra of Continuous Functions

video tutorial00:06:40
Algebra of Continuous Functions

video tutorial00:14:19
Algebra of Continuous Functions

video tutorial01:07:16

RELATED QUESTIONS

Find the relationship between a and b so that the function f defined by $f (x) = {\begin{cases} a x + 1 & if x \leq 3 \\ b x + 3 & if x > 3 \end{cases}$ is continuous at x = 3.

Discuss the continuity of the following function:

f (x) = sin x × cos x

Discuss the continuity of the cosine, cosecant, secant and cotangent functions,

Find the values of k so that the function f is continuous at the indicated point.

$f (x) = {\begin{cases} \frac{k \cos x}{π - 2 x} & , if x \neq \frac{π}{2} \\ 3 & , if x = \frac{π}{2} \end{cases} at x = \frac{π}{2}$

Find the values of k so that the function f is continuous at the indicated point.

$f (x) = {\begin{cases} k x + 1 & if x \leq π \\ \cos x & if x > π \end{cases} at x = π$

Find the values of a so that the function

f (x) = {\begin{cases} a x + 5, i f & x \leq 2 \\ x - 1, i f & x > 2 \end{cases} is continuous at x = 2 .

If $f (x) = \frac{2 x + 3 sin x}{3 x + 2 sin x}, x \neq 0$ If f(x) is continuous at x = 0, then find f (0).

If $f (x) = {\begin{cases} 2 x^{2} + k, & if x \geq 0 \\ - 2 x^{2} + k, & if x < 0 \end{cases}$ then what should be the value of k so that f(x) is continuous at x = 0.

Prove that the function $f (x) = {\begin{cases} \frac{\sin x}{x}, & x < 0 \\ x + 1, & x \geq 0 \end{cases}$ is everywhere continuous.

Discuss the continuity of the function

f (x) = {\begin{cases} \frac{x}{| x |}, & x \neq 0 \\ 0, & x = 0 \end{cases} .

Find the points of discontinuity, if any, of the following functions: $f (x) = {\begin{cases} \frac{\sin x}{x}, & if x < 0 \\ 2 x + 3, & x \geq 0 \end{cases}$

In the following, determine the value of constant involved in the definition so that the given function is continuou: $f (x) = {\begin{cases} 2, & if x \leq 3 \\ a x + b, & if 3 < x < 5 \\ 9, & if x \geq 5 \end{cases}$

The function $f (x) = {\begin{cases} x^{2} / a, & if 0 \leq x < 1 \\ a, & if 1 \leq x < \sqrt{2} \\ \frac{2 b^{2} - 4 b}{x^{2}}, & if \sqrt{2} \leq x < \infty \end{cases}$ is continuous on (0, ∞), then find the most suitable values of a and b.

If $f (x) = {\begin{cases} \frac{x}{\sin 3 x}, & x \neq 0 \\ k, & x = 0 \end{cases}$ is continuous at x = 0, then write the value of k.

If the function $f (x) = \frac{\sin 10 x}{x}, x \neq 0$ is continuous at x = 0, find f (0).

If $f (x) = (\binom{\frac{1 - \cos x}{x^{2}}, x \neq 0}{k, x = 0})$ is continuous at x = 0, find k.

If f (x) = (x + 1)^cot x be continuous at x = 0, then f (0) is equal to

If $f (x) = {\begin{cases} \frac{\log (1 + a x) - \log (1 - b x)}{x}, & x \neq 0 \\ k, & x = 0 \end{cases}$ and f (x) is continuous at x = 0, then the value of k is

The function

f (x) = {\begin{cases} x^{2} / a, & 0 \leq x < 1 \\ a, & 1 \leq x < \sqrt{2} \\ \frac{2 b^{2} - 4 b}{x^{2}}, & \sqrt{2} \leq x < \infty \end{cases}

is continuous for 0 ≤ x < ∞, then the most suitable values of a and b are

If $f (x) = \frac{1 - \sin x}{{(π - 2 x)}^{2}},$ when x ≠ π/2 and f (π/2) = λ, then f (x) will be continuous function at x= π/2, where λ =

If the function f (x) defined by $f (x) = {\begin{cases} \frac{\log (1 + 3 x) - \log (1 - 2 x)}{x}, & x \neq 0 \\ k, & x = 0 \end{cases}$ is continuous at x = 0, then k =

If $f (x) = {\begin{cases} \frac{1 - \cos 10 x}{x^{2}}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x}}{\sqrt{625 + \sqrt{x}} - 25}, & x > 0 \end{cases}$ then the value of a so that f (x) may be continuous at x = 0, is

If f is defined by $f (x) = x^{2} - 4 x + 7$ , show that $f^{'} (5) = 2 f^{'} (\frac{7}{2})$

If $f (x) = \sqrt{x^{2} + 9}$ , write the value of

lim_{x \to 4} \frac{f (x) - f (4)}{x - 4} .

The function $f (x) = \frac{\sin (π [x - π])}{4 + {[x]}^{2}}$ , where [⋅] denotes the greatest integer function, is

Let f (x) = a + b |x| + c |x|⁴, where a, b, and c are real constants. Then, f (x) is differentiable at x = 0, if

If f(x) = 2x and g(x) = $\frac{x^{2}}{2} + 1$ , then which of the following can be a discontinuous function ______.

The function f(x) = $\frac{4 - x^{2}}{4 x - x^{3}}$ is ______.

lim_{x \to 0} \frac{1 - cos x}{x}

is equal to ____________.

$lim_{x \to π} \frac{1 + {cos}^{2} x}{{(x - π)}^{2}}$ is equal to ____________.

$lim_{x \to 0} \frac{1 - cos x}{x sin x}$ is equal to ____________.

For what value of $k$ the following function is continuous at the indicated point

$f (x) = {\begin{array}{l} k x + 1, & if x \leq π \\ \cos x, & if x > π \end{array}$ at = $π$

Discuss the continuity of the following function:

f(x) = sin x + cos x

Discuss the continuity of the following function:

f(x) = sin x – cos x

Examine sin |x| is a continuous function. - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [3]

RELATED QUESTIONS

Select a course

Examine sin |x| is a continuous function. - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [3]

RELATED QUESTIONS

Select a course

Solution