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Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}\frac{\sin x}{x}, & \text{ if } x < 0 \\ 2x + 3, & x \geq 0\end{cases}\]
Concept: undefined >> undefined
Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}\frac{\sin x}{x} + \cos x, & \text{ if } x \neq 0 \\ 5 , & \text { if } x = 0\end{cases}\]
Concept: undefined >> undefined
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In the following, determine the value of constant involved in the definition so that the given function is continuou: \[f\left( x \right) = \begin{cases}\frac{\sin 2x}{5x}, & \text{ if } x \neq 0 \\ 3k , & \text{ if } x = 0\end{cases}\]
Concept: undefined >> undefined
In the following, determine the value of constant involved in the definition so that the given function is continuou: \[f\left( x \right) = \begin{cases}kx + 5, & \text{ if } x \leq 2 \\ x - 1, & \text{ if } x > 2\end{cases}\]
Concept: undefined >> undefined
In the following, determine the value of constant involved in the definition so that the given function is continuou: \[f\left( x \right) = \begin{cases}k( x^2 + 3x), & \text{ if } x < 0 \\ \cos 2x , & \text{ if } x \geq 0\end{cases}\]
Concept: undefined >> undefined
In the following, determine the value of constant involved in the definition so that the given function is continuou: \[f\left( x \right) = \begin{cases}2 , & \text{ if } x \leq 3 \\ ax + b, & \text{ if } 3 < x < 5 \\ 9 , & \text{ if } x \geq 5\end{cases}\]
Concept: undefined >> undefined
In the following, determine the value of constant involved in the definition so that the given function is continuou: \[f\left( x \right) = \begin{cases}4 , & \text{ if } x \leq - 1 \\ a x^2 + b, & \text{ if } - 1 < x < 0 \\ \cos x, &\text{ if }x \geq 0\end{cases}\]
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
The function f(x) is defined as follows:
If f is continuous on [0, 8], find the values of a and b.
Concept: undefined >> undefined
If \[f\left( x \right) = \frac{\tan\left( \frac{\pi}{4} - x \right)}{\cot 2x}\]
for x ≠ π/4, find the value which can be assigned to f(x) at x = π/4 so that the function f(x) becomes continuous every where in [0, π/2].
Concept: undefined >> undefined
Discuss the continuity of f(x) = sin | x |.
Concept: undefined >> undefined
Show that the function g (x) = x − [x] is discontinuous at all integral points. Here [x] denotes the greatest integer function.
Concept: undefined >> undefined
Discuss the continuity of the following functions:
(i) f(x) = sin x + cos x
(ii) f(x) = sin x − cos x
(iii) f(x) = sin x cos x
Concept: undefined >> undefined
Show that f (x) = cos x2 is a continuous function.
Concept: undefined >> undefined
Show that f (x) = | cos x | is a continuous function.
Concept: undefined >> undefined
What happens to a function f (x) at x = a, if
Concept: undefined >> undefined
If \[f\left( x \right) = \begin{cases}\frac{x}{\sin 3x}, & x \neq 0 \\ k , & x = 0\end{cases}\] is continuous at x = 0, then write the value of k.
Concept: undefined >> undefined
If the function \[f\left( x \right) = \frac{\sin 10x}{x}, x \neq 0\] is continuous at x = 0, find f (0).
Concept: undefined >> undefined
Determine whether \[f\left( x \right) = \binom{\frac{\sin x^2}{x}, x \neq 0}{0, x = 0}\] is continuous at x = 0 or not.
Concept: undefined >> undefined
If \[f\left( x \right) = \binom{\frac{1 - \cos x}{x^2}, x \neq 0}{k, x = 0}\] is continuous at x = 0, find k.
Concept: undefined >> undefined
