The angle at which curve y - ke kx intersects the y axis is A- tan -1k2B- -1k2C- sin -11-k2D- None of these

The correct option is B y = ke^kx cuts the y axis at x = 0 dy/dx = k^2 e^kx at x = 0 dy/dx = k^2 α = tan^ 1(k^2) this is angle made by x axis,so angle mad ...

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Standard XII

Mathematics

Equation of Tangent at a Point (x,y) in Terms of f'(x)

The angle at ...

Question

The angle at which curve $y = k e^{k x}$ intersects the y axis is

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None of these

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Solution

The correct option is B
y = $k e^{k x}$ cuts the y-axis at x = 0
$\frac{d y}{d x} = k^{2} e^{k x}$
at x = 0
$\frac{d y}{d x} = k^{2}$
$α = t a n^{- 1} (k^{2})$ this is angle made by x- axis,so angle made by y-axis is $\frac{π}{2} - t a n^{- 1} (k^{2})$
or $c o t^{- 1} (k^{2})$

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The angle at which curve y = kekx intersects the y axis is

The correct option is B y = kekx cuts the y-axis at x = 0 dydx=k2ekx at x = 0 dydx=k2 α=tan−1(k2) this is angle made by x- axis,so angle made by y-axis is π2−tan−1(k2) or cot−1(k2)

The angle at which curve $y = k e^{k x}$ intersects the y axis is

The correct option is B
y = $k e^{k x}$ cuts the y-axis at x = 0
$\frac{d y}{d x} = k^{2} e^{k x}$
at x = 0
$\frac{d y}{d x} = k^{2}$
$α = t a n^{- 1} (k^{2})$ this is angle made by x- axis,so angle made by y-axis is $\frac{π}{2} - t a n^{- 1} (k^{2})$
or $c o t^{- 1} (k^{2})$