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1 Unit 1: Pure Mathematics A

A curve has the equation $y = e^{2x}$

Find, in terms of $a$ , the equation of the tangent to the curve at the point $a, e^{2a})$

[3]

Find the value of $a\,$ for which this tangent passes through the origin.

[2]

Hence, find the set of values of $m\,$ for which the equation $e^{2x} = mx$ has no real solutions.

[3]

1 Unit 1: Pure Mathematics A Questions

A curve has the equation $y = e^{2x}$

Find, in terms of $a$ , the equation of the tangent to the curve at the point $a, e^{2a})$

[3]

Find the value of $a\,$ for which this tangent passes through the origin.

[2]

Hence, find the set of values of $m\,$ for which the equation $e^{2x} = mx$ has no real solutions.

[3]