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प्रश्न
A continuous function can have some points where limit does not exist.
पर्याय
True
False
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उत्तर
This statement is False.
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संबंधित प्रश्न
Examine the following function for continuity:
f(x) = x – 5
Show that
is discontinuous at x = 0.
Show that
\[f\left( x \right) = \begin{cases}\frac{\sin 3x}{\tan 2x} , if x < 0 \\ \frac{3}{2} , if x = 0 \\ \frac{\log(1 + 3x)}{e^{2x} - 1} , if x > 0\end{cases}\text{is continuous at} x = 0\]
Determine the value of the constant k so that the function
\[f\left( x \right) = \left\{ \begin{array}{l}\frac{x^2 - 3x + 2}{x - 1}, if & x \neq 1 \\ k , if & x = 1\end{array}\text{is continuous at x} = 1 \right.\]
Determine the values of a, b, c for which the function f(x) = `{((sin(a + 1)x + sin x)/x, "for" x < 0),(x, "for" x = 0),((sqrt(x + bx^2) - sqrtx)/(bx^(3"/"2)), "for" x > 0):}` is continuous at x = 0.
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point;
For what value of k is the following function continuous at x = 2?
Determine if \[f\left( x \right) = \begin{cases}x^2 \sin\frac{1}{x} , & x \neq 0 \\ 0 , & x = 0\end{cases}\] is a continuous function?
Define continuity of a function at a point.
If \[f\left( x \right) = \left| \log_{10} x \right|\] then at x = 1
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The value of b for which the function
If \[f\left( x \right) = \left\{ \begin{array}a x^2 + b , & 0 \leq x < 1 \\ 4 , & x = 1 \\ x + 3 , & 1 < x \leq 2\end{array}, \right.\] then the value of (a, b) for which f (x) cannot be continuous at x = 1, is
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Discuss the continuity and differentiability of
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If \[f\left( x \right) = \left| \log_e x \right|, \text { then}\]
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= `x^3 + a + b, for x > 0
and f (1) = 2, then find a and b.
Find the value of 'k' if the function
f(x) = `(tan 7x)/(2x)`, for x ≠ 0.
= k for x = 0.
is continuous at x = 0.
Examine the continuity of the following function :
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If y = ( sin x )x , Find `dy/dx`
Examine the continuity of the followin function :
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The function given by f (x) = tanx is discontinuous on the set ______.
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f(x) = `{{:(3x + 5",", "if" x ≥ 2),(x^2",", "if" x < 2):}` at x = 2
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Show that f(x) = |x – 5| is continuous but not differentiable at x = 5.
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