Find the angle at which the curve `y=K e^(K x)` intersects the y-axis.

(i) Find the point at which the circle x^(2) + y^(2) = 32 intersects the positive x-axis. (ii) Shade the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x^(2) + y^(2) = 32 . (iii) Using integration, find the area of the shaded region.

Find the angle at which the parabolas y^2=4x and x^2=32 y intersect.

A line is inclined to the x-axis at 45^@ and y-axis at 60^@ . Find the angle at which the line is inclined to z-axis.

Tangent is drawn at the point (x_i ,y_i) on the curve y=f(x), which intersects the x-axis at (x_(i+1),0) . Now, again a tangent is drawn at (x_(i+1,)y_(i+1)) on the curve which intersect the x-axis at (x_(i+2,)0) and the process is repeated n times, i.e. i=1,2,3dot,ndot If x_1,x_2,x_3,ddot,x_n from an arithmetic progression with common difference equal to (log)_2e and curve passes through (0,2)dot Now if curve passes through the point (-2, k), then the value of k is____

Tangent is drawn at the point (x_i ,y_i) on the curve y=f(x), which intersects the x-axis at (x_(i+1),0) . Now, again a tangent is drawn at (x_(i+1,)y_(i+1)) on the curve which intersect the x-axis at (x_(i+2,)0) and the process is repeated n times, i.e. i=1,2,3dot,ndot If x_1,x_2,x_3,ddot,x_n from an arithmetic progression with common difference equal to (log)_2e and curve passes through (0,2)dot Now if curve passes through the point (-2, k), then the value of k is____

Find the length of sub-tangent to the curve y=e^(x//a)

The curve y=e^(x) is _________

Find the area under the curve y = x^(2) above x-axis between the lines x = 6 and x = 4.

If the eccentricity of the curve for which tangent at point P intersects the y-axis at M such that the point of tangency is equidistant from M and the origin is e , then the value of 5e^2 is___

If the eccentricity of the curve for which tangent at point P intersects the y-axis at M such that the point of tangency is equidistant from M and the origin is e , then the value of 5e^2 is___