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Question

The tangent to the curve $$y=e^{2x}$$ at the point $$(0, 1)$$ meets x-axis at?


A
(0,1)
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B
(12,0)
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C
(2,0)
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D
(0,2)
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Solution

The correct option is C $$(2, 0)$$
solution -  equation of curve is y=$$e^{2x}$$
tangent to the curve is 
$$\frac{dy}{dx}=2e^{2x}$$
$$(\frac{de^{x}}{dx}=e^{x})$$
At points (0,1), the tangent  is 
$$(\frac{dy}{dx})_{(0,1)}=2e^{2(0)}$$
$$(\frac{dy}{dx})_{(0,1)}=2e^{0}$$           $$[e^{0}=1]$$
$$\frac{dy}{dx}_{0,1}=2$$
when the slope is 2, and solve the tangent 
meets y axis the coordinate is 0,
Hence the tangent meets the x axis at (2,0)

1176120_1294135_ans_11a7c6cc3b38459bb3209773aa2a4a3f.jpg

Mathematics

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