# Calculus Techniques Interactive Diagrams

## Tangent line given function and \(x\)-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

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## 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 \(\leq t\leq\))

- 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 to 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

Last modified: Tue Jul 21 17:14:16 AWST 2020