Calculus

Parabola given by the function f(x) = x^2

Let (r, r^2) be an arbitrary point on the parabola f(x) = x^2. Show that the equation of the tangent line to the graph of f(x) at (r, r^2) is given by...

100%

Gradient for functions in two variables

Find ∇f(1, 1) for the function in two variables f(x, y) = x^2 + y^2.

Is there an easy formula to get the indefinite sum of x^n?

e.g. sum for 1 to n is n(n+1)/2. Another example, formula for integration where x^n becomes [1/(n+1)]x^(n+1).

Gradient for functions in two variables

Find ∇f(1, 1) for the function in two variables f(x, y) = x^2 + y^2.

Parabola given by the function f(x) = x^2

Let (r, r^2) be an arbitrary point on the parabola f(x) = x^2. Show that the equation of the tangent line to the graph of f(x) at (r, r^2) is given by...

100%

Is there an easy formula to get the indefinite sum of x^n?

e.g. sum for 1 to n is n(n+1)/2. Another example, formula for integration where x^n becomes [1/(n+1)]x^(n+1).