Advertisements
Advertisements
प्रश्न
The function f (x) = 1 + |cos x| is
विकल्प
continuous no where
continuous everywhere
not differentiable at x = 0
not differentiable at x = n π, n ∈ Z
Advertisements
उत्तर
(b) continuous everywhere
Graph of the function f (x) = 1 + |cos x| is as shown below:
From the graph, we can see that f (x) is everywhere continuous but not differentiable at
APPEARS IN
संबंधित प्रश्न
A function f (x) is defined as
f (x) = x + a, x < 0
= x, 0 ≤x ≤ 1
= b- x, x ≥1
is continuous in its domain.
Find a + b.
Discuss the continuity of the following function:
f(x) = sin x × cos x
Find the value of k so that the function f is continuous at the indicated point.
f(x) = `{((kcosx)/(pi-2x)", if" x != pi/2),(3", if" x = pi/2):}` at x = `"pi/2`
Find the value of k so that the function f is continuous at the indicated point.
f(x) = `{(kx +1", if" x<= pi),(cos x", if" x > pi):}` at x = π
Find the values of a and b such that the function defined by f(x) = `{(5", if" x <= 2),(ax +b", if" 2 < x < 10),(21", if" x >= 10):}` is a continuous function.
Show that the function defined by f(x) = cos (x2) is a continuous function.
Examine that sin |x| is a continuous function.
Determine the value of the constant k so that the function
\[f\left( x \right) = \begin{cases}\frac{\sin 2x}{5x}, if & x \neq 0 \\ k , if & x = 0\end{cases}\text{is continuous at x} = 0 .\]
Find the value of k if f(x) is continuous at x = π/2, where \[f\left( x \right) = \begin{cases}\frac{k \cos x}{\pi - 2x}, & x \neq \pi/2 \\ 3 , & x = \pi/2\end{cases}\]
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; \[f\left( x \right) = \begin{cases}(x - 1)\tan\frac{\pi x}{2}, \text{ if } & x \neq 1 \\ k , if & x = 1\end{cases}\] at x = 1at x = 1
If \[f\left( x \right) = \begin{cases}\frac{x^2}{2}, & \text{ if } 0 \leq x \leq 1 \\ 2 x^2 - 3x + \frac{3}{2}, & \text P{ \text{ if } } 1 < x \leq 2\end{cases}\]. Show that f is continuous at x = 1.
In the following, determine the value of constant involved in the definition so that the given function is continuou: \[f\left( x \right) = \begin{cases}kx + 5, & \text{ if } x \leq 2 \\ x - 1, & \text{ if } x > 2\end{cases}\]
In the following, determine the value of constant involved in the definition so that the given function is continuou: \[f\left( x \right) = \begin{cases}4 , & \text{ if } x \leq - 1 \\ a x^2 + b, & \text{ if } - 1 < x < 0 \\ \cos x, &\text{ if }x \geq 0\end{cases}\]
The function \[f\left( x \right) = \begin{cases}x^2 /a , & \text{ if } 0 \leq x < 1 \\ a , & \text{ if } 1 \leq x < \sqrt{2} \\ \frac{2 b^2 - 4b}{x^2}, & \text{ if } \sqrt{2} \leq x < \infty\end{cases}\] is continuous on (0, ∞), then find the most suitable values of a and b.
Show that the function g (x) = x − [x] is discontinuous at all integral points. Here [x] denotes the greatest integer function.
Show that f (x) = cos x2 is a continuous function.
Show that f (x) = | cos x | is a continuous function.
\[f\left( x \right) = \begin{cases}\frac{\left| x^2 - x \right|}{x^2 - x}, & x \neq 0, 1 \\ 1 , & x = 0 \\ - 1 , & x = 1\end{cases}\] then f (x) is continuous for all
Let \[f\left( x \right) = \left\{ \begin{array}\\ \frac{x - 4}{\left| x - 4 \right|} + a, & x < 4 \\ a + b , & x = 4 \\ \frac{x - 4}{\left| x - 4 \right|} + b, & x > 4\end{array} . \right.\]Then, f (x) is continuous at x = 4 when
If \[f\left( x \right) = \begin{cases}\frac{1 - \cos x}{x \sin x}, & x \neq 0 \\ \frac{1}{2} , & x = 0\end{cases}\]
then at x = 0, f (x) is
The function f(x) = `(4 - x^2)/(4x - x^3)` is ______.
`lim_("x" -> 0) ("x cos x" - "log" (1 + "x"))/"x"^2` is equal to ____________.
Let `"f" ("x") = ("In" (1 + "ax") - "In" (1 - "bx"))/"x", "x" ne 0` If f (x) is continuous at x = 0, then f(0) = ____________.
Let f(x) = `{{:(5^(1/x), x < 0),(lambda[x], x ≥ 0):}` and λ ∈ R, then at x = 0
For what value of `k` the following function is continuous at the indicated point
`f(x) = {{:(kx^2",", if x ≤ 2),(3",", if x > 2):}` at x = 2
For what value of `k` the following function is continuous at the indicated point
`f(x) = {{:(kx + 1",", if x ≤ pi),(cos x",", if x > pi):}` at = `pi`
The function f(x) = x |x| is ______.
Discuss the continuity of the following function:
f(x) = sin x – cos x
If \[f\] and \[g\] are continuous at \[x=c\], which collection is continuous at \[x=c\]?
If \[g\] is continuous and \[g(x)\neq 0\], which function is continuous?
For \[f(x)=\frac{p(x)}{q(x)}\], where \[p(x)\] and \[q(x)\] are polynomial functions, where is \[f\] continuous?
If \[f\] is continuous, which scalar multiple is continuous?
What is the definition of the composite function \[f\circ g\]?
Let \[g(x)=\sin x\] and \[h(x)=x^2\]. Which expression equals \[(g\circ h)(x)\]?
Why is \[g(x)=1-x+|x|\] continuous?
