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## Tangent line given function and -coordinate

Note that the results shown are based on numeric approximations and should be taken as illustrative only.

Find the equation of the tangent to the curve (f(x)=) where (x=)

- Evaluate (f(x)) to determine coordinates of the point the tangent must pass through
- Determine (f'(x))
- Evaluate (f'(x)) at the given value of (x) to determine gradient of tangent line
- Use gradient and point give the equation of the line

## Tangent line from parametric equations

Find the equation of the tangent to the curve given by parametric equations (x(t)=) and (y(t)=) where (t=)

(Graph over the domain (leq tleq))

- Evaluate (x(t)) and (y(t))to determine coordinates of the point the tangent must pass through (A:left(x(t),y(t)right))
- Determine (frac{dy}{dx}=frac{dy}{dt}frac{dt}{dx})
- Evaluate (frac{dy}{dx}) at the given value of (t) to determine gradient of tangent line
- Use gradient and point give the equation of the line

## Area under a curve

Note that the results shown are based on numeric approximations and should be taken as illustrative only.

Find the area between the curve (f(x)=) and the (x)-axis over the interval to

## Area between curves

Find the area between the curve (f(x)=) and (g(x)=) over the interval to