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Find the limit of $\left(\frac{1-\cos\left(x\right)}{x}\right)^2$ as $x$ approaches 0

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 Solution

 Videos

Derivatives of sec(x) and csc(x) | Derivative rules | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=TDJ5nXWEkWM

Calculus - Evaluating a limit by rationalizing the radical, lim(x tends to 0) (sqrt(x + 1) - 1)/x

https://www.youtube.com/watch?v=v8dIvXm03dw

Limit of (sin x)/x as x approaches 0

https://www.youtube.com/watch?v=5xitzTutKqM

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=1ct7LUx23io

Squeeze Theorem

https://www.youtube.com/watch?v=lVIb9iJ-rRI

 Function Plot

Plotting: $\left(\frac{1-\cos\left(x\right)}{x}\right)^2$

 Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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