# Find the curvature kappa of the plane curve at the given value of the parameter. r(t) = t i +...

## Question:

Find the curvature kappa of the plane curve at the given value of the parameter.

{eq}\mathrm{r}(t) = t \, \mathrm{i} + \frac{1}{36} t^3 \, \mathrm{j}, \; t = 3 {/eq}

## Curvature of a Vector Curve:

Use the following formula to find the curvature of vector function. {eq}\displaystyle k=\frac{\left|r'(t)\times r''(t)\right|} {\left|r'(t)\right|^3}\\ {/eq}

Therefore, find the first derivative of the given vector function and the second derivative of the vector function at the given value of t. The term in the denominator is magnitude of the vector cross product of the first and the second derivative. Find the required magnitude of the derivatives and put them in the equation. You will get the curvature.

## Answer and Explanation: 1

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{eq}\mathrm{r}(t) = t \, \mathrm{i} + \frac{1}{36} t^3 \, \mathrm{j}, \; t = 3 {/eq}.

Find the first derivative and the second derivative:

{eq}\beg...

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#### Learn more about this topic: Broad Differentiation Strategy: Definition & Examples

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Chapter 6 / Lesson 39
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Broad differentiation strategy is pursued by companies seeking to stand out as unique. In this lesson, you'll learn more about the strategy and some businesses using it successfully.