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Question
The tangent to the curve y = e2x at the point (0, 1) meets x-axis at ______.
Options
(0, 1)
`(- 1/2, 0)`
(2, 0)
(0, 2)
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Solution
The tangent to the curve y = e2x at the point (0, 1) meets x-axis at `(- 1/2, 0)`.
Explanation:
Equation of the curve is y = e2x
Slope of the tangent `"dy"/"dx"` = 2e2x
⇒ `"dy"/"dx"_(0, 1)` = 2 · e0 = 2
∴ Equation of tangent to the curve at (0, 1) is
y –1 = 2(x – 0)
⇒ y – 1 = 2x
⇒ y – 2x = 1
Since the tangent meets x-axis where y = 0
∴ 0 – 2x = 1
⇒ x = `(-1)/2`
So the point is `(- 1/2, 0)`.
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