If f x is a continuous real-valued function satisfying lim x - f x - a- where a is a finite real number- then the value of lim x - f - x isA- 1B- 0C- doesn-t existD- depends on -a-

The correct option is B 0When x→∞, the function f(x) attains a finite real value 'a' nbsp; ⇒ y=a is the asymptote of f(x). ∴lim_x→∞f'(x)= slope of asymptot ...

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Standard XII

Mathematics

Equation of Tangent at a Point (x,y) in Terms of f'(x)

If f x is a c...

Question

If $f (x)$ is a continuous real-valued function satisfying $lim x \to \infty f (x) = a,$ where $a$ is a finite real number, then the value of $lim x \to \infty f^{'} (x)$ is

1

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0

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doesn't exist

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depends on '

a

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Solution

The correct option is B $0$
When $x \to \infty,$ the function $f (x)$ attains a finite real value ' $a$ '
$\Rightarrow y = a$ is the asymptote of $f (x) .$

$∴ lim x \to \infty f^{'} (x) = slope of asymptote = 0$

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Similar questions

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If f(x) is a continuous real-valued function satisfying limx→∞f(x)=a , where a is a finite real number, then the value of limx→∞f′(x) is

The correct option is B 0When x→∞, the function f(x) attains a finite real value 'a' ⇒y=a is the asymptote of f(x). ∴limx→∞f′(x)= slope of asymptote = 0

If $f (x)$ is a continuous real-valued function satisfying $lim x \to \infty f (x) = a,$ where $a$ is a finite real number, then the value of $lim x \to \infty f^{'} (x)$ is

The correct option is B $0$
When $x \to \infty,$ the function $f (x)$ attains a finite real value ' $a$ '
$\Rightarrow y = a$ is the asymptote of $f (x) .$

$∴ lim x \to \infty f^{'} (x) = slope of asymptote = 0$