Use Mean value Theorem to show that |sinx-siny|≤|x-y| скачать в хорошем качестве

Use Mean value Theorem to show that |sinx-siny|≤|x-y|

Use Mean value Theorem to show that |sinx-siny|≤|x-y| The Mean Value Theorem is a fundamental theorem in calculus that states that for a differentiable function f(x) on an interval [a, b], there exists at least one point c in (a, b) such that the slope of the tangent line at c is equal to the average rate of change of f(x) over [a, b].    • BS Bsc calculus math Exercise 6.2 Question...   Solve Dy/dx+√(1-y^2)/√(1-x^2)=0    • How to solve differential equation dy/dx+√...   Using the Mean Value Theorem, we can prove the inequality |sinx-siny|≤|x-y| as follows: Let f(x) = sin(x) and consider two points x and y on the interval [a, b]. By the Mean Value Theorem, there exists a point c between x and y such that: f'(c) = (f(x) - f(y))/(x - y) Since f'(x) = cos(x), we have: |cos(c)| = |(sin(x) - sin(y))/(x - y)| Since |cos(x)| ≤ 1 for all x, we can simplify the inequality to: |(sin(x) - sin(y))/(x - y)| ≤ 1 Multiplying both sides by |x - y|, we get: |sin(x) - sin(y)| ≤ |x - y| Thus, we have proved that |sinx-siny|≤|x-y| using the Mean Value Theorem. Mean value theorem, derivative, differentiable, continuous, absolute value, sine function, inequality, proof, interval, function. Hashtags: #MeanValueTheorem #ncert #ncertsolutions #Calculus #Inequality #minut #SineFunction #TangentLine #Mathematics Keywords: mean value theorem, calculus, basic introduction, practice problems, problems, examples, derivatives ,