2001 A-Level H2 Mathematics

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Question 2Graphing Techniques

Find the equation of the tangent to the curve $y={{e}^{x}}$ at the point where $x=a$. Hence find the equation of the tangent to the curve $y={{e}^{x}}$ which passes through the origin. The straight line $y=mx$ intersects the curve $y={{e}^{x}}$ in two distinct points. Write down an inequality for $m$.

Final Answer:

${y=ex}$, ${m>e}$