# Let $y = e^{x}$ then the equation of the tangent at (0, 1) will be? Option 1) $y = 2x + 3$ Option 2) $y = 2x + 1$ Option 3) $y = x + 1$ Option 4) $y - 3x = 1$

H Himanshu

As we have learnt,

Equation of the tangent -

To find the equation of the tangent we need either one slope + one point or two points.

$\therefore \:\:(y-y_{\circ})=m(x_{\circ }-y_{\circ })$

$or\:\:(y-y_{2})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{2})$

- wherein

Where  $(x_{\circ},y_{\circ})$   is the point on the curve and M = MT  slope of tangent.

$\frac{\mathrm{d} y}{\mathrm{d} x} = e^{x} \Rightarrow$$\frac{\mathrm{d} y}{\mathrm{d} x} = e^{x} \Rightarrow \frac{\mathrm{d} y}{\mathrm{d} x}$ at (0, 1) = $= e^{0} = 1 =$ slope of tangent

Therefore, equation of tangent = $(y-1) = 1(x-0) \Rightarrow y = x + 1$

Option 1)

$y = 2x + 3$

Option 2)

$y = 2x + 1$

Option 3)

$y = x + 1$

Option 4)

$y - 3x = 1$

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