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Find \cot \theta, given that \cos \theta = -\frac{2}{3} and \theta is in Quadrant III. Show all work without a calculator. Simplify and find the exact value of cot( 1/2 tan^{-1} 2). Assume x is greater than 0. Rationalize denominators. ...
Find the following limit: {eq}\lim_{x \to -1} \frac{3 + 2x}{2x - 2} {/eq} Limits: The limit is a particular value to which a function approaches as the input of that function approaches a given value (in the above question, we need to find the limit of the functi...
Derivatives of Inverse Functions Function must be one-to-one If f is differentiable at every point of an interval and df/dx is never zero on the interval, then f has an inverse and f -1 is differentiable at every point. Derivative of arcsin...
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The differentiation of the function can be easily found using the standard formula. There is another method to find the derivative, that is by the use of the first principle rule of differentiation, we need to use the concepts of limits ...
We will have to use implicit differentiation twice to find the wanted derivative. Recall that implicit differentiation is a rather unnecessary name for a direct application of the chain rule. All we are really doing here is taking a couple derivatives and applying the chain rul...
Differentiation is the process of finding the derivative of a function. Usually, differentiation can be done explicitly. However, if we are given an implicit equation or function, we may need to use implicit differentiation. Answer and Explanation: Solution (a): Here the give...
Evaluating Definite Integrals Using the Fundamental Theorem from Chapter 16 / Lesson 2 4.2K In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using th...
Use a graphing calculator to display at least two members of the family of the curves and at least two of the orthogona Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Show that the given families of curves are...