Question
where a,b,c are real and non-zero=
Hint:
The initial form for the limit is indeterminate
to the power of infinity So, use the formula. In this question, we have to find value of
.
The correct answer is: ![left parenthesis a b c right parenthesis to the power of 1 third end exponent](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x](data:image/png;base64,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)
where a,b,c are real and non-zero
this is known as an indeterminate form, because it is unknown. One to the power infinity is unknown because infinity itself is endless. Take a look at some examples of indeterminate forms. To solve this limit we will use the following formula -
![Error converting from MathML to accessible text.](data:image/png;base64,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![Error converting from MathML to accessible 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)
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
Related Questions to study
Which graph present the variation of surface tension with temperature over small temperature ranges for coater.
Which graph present the variation of surface tension with temperature over small temperature ranges for coater.
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
A soap bubble is blown with the help of a mechanical pump at the mouth-of a tube the pump produces a certain increase per minute in the volume of the bubble irrespective of its internal pressure the graph between the pressure inside the soap bubble and time t will be
A soap bubble is blown with the help of a mechanical pump at the mouth-of a tube the pump produces a certain increase per minute in the volume of the bubble irrespective of its internal pressure the graph between the pressure inside the soap bubble and time t will be
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
The correct relation is.
The correct relation is.
A vessel whose bottom has round holes with diameter of 0.1 mm is filled with water. The maximum height to which the water can be filled without leakage is
(S.T. of water )
A vessel whose bottom has round holes with diameter of 0.1 mm is filled with water. The maximum height to which the water can be filled without leakage is
(S.T. of water )
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or