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We differentiate our equation with respect to x to find that 2x - 2y(dy/dx) = 0, and rearrange to find that dy/dx = x/y. We set P = (x, y). The slope of OP is given by y/x, and the slope of the tangent at...

After sketching a diagram of the curve and the solid for clarity, we see that we need to use the formula V = π∫ y² dx (with upper and lower bounds of 3π/4 and π/4 respectively) to calculate the...

First thing first, we should always write down the equation of a straight line (which is y = mx + c) as this will be important for this question.In order to find the equation of the strai...

Use product rule. d(uv)/dx = u dv/dx +v du/dxu=x du/dx=1v=e^x dv/dx=e^x
d(xe^x)/dx = xe^x + e^x.1 = e^x(x+1)

To find the value of w, let x = w and y = -32. Substitute these values into the equation of the curve, C: y = (2x-3)^5 => -32 = (2(w) - 3 )^5. Note: the symbol, =>, means "implies that." F...