Use calculus to evaluate
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Use calculus to evaluate
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Integrate
Use calculus to find the exact value of
.
Find an expression for given that
.
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Given the identity , show that
Hence find the exact value of
.
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Find the exact value of
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Integrate
Use calculus to find the exact value of
.
Find an expression for given that
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Find an expression for given that
.
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Find an expression for given that
giving your answer as a single logarithm.
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This topic pack contains questions on the following:
Find the integral
Use calculus to evaluate
Find an expression for given that
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Integrate
Use calculus to find the value of
Find an expression for given that
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Given that
use calculus to find the exact value of
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Find
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Given that , find .
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Integrate
Find an expression for given that
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Find an expression for given that
Find an expression for given that
Use calculus to find the exact value of
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Use the identity
to show that
Hence, or otherwise, find the integral
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Show that
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Given that the graph of passes through the point and that
Find
Explain why must be excluded from the domain of .
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Show that
where is a constant.
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Find the integral
Find an expression for given that
Use calculus to evaluate
giving your answer as a single logarithm.
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Integrate
Use calculus to find the value of
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Show that, for (where is an integer),
Use calculus and your result from part [a] to show that
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Use calculus to find the exact value of
.
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Use calculus to show that
.
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Find an expression for given that
Find an expression for given that
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Show that
Hence, or otherwise, find an expression for
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Write in the form , where are all linear functions of .
Hence show that
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Given that and that show that
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Given
and that the graph of passes through the point find .
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Find an expression for given that
Integrate
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Find
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Show that
where is a constant, and is the constant of integration.
Use calculus to find the exact value of
writing your answer in the form , where and are rational numbers to be found.
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Use calculus to find the value of
giving your answer in the form , where and are prime numbers to be found.
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Show that
Hence, or otherwise, find the exact value of
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Show that
where and are constants, and .
Using your working from part [a], or otherwise, evaluate
giving your answer in terms of , where are constants, and .
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Show that
Hence, or otherwise, find an expression for given that
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Show that there are no positive values of and that satisfy the equation
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Given that
and also that
find .
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Given that , show that
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