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  1. en.wikipedia.org › wiki › DerivativeDerivative - Wikipedia

    Hace 4 días · The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function 's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear ...

  2. Hace 3 días · t. e. In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.

  3. 23 de abr. de 2024 · (A) x = -2 x = −2. (B) x = -4 x = −4. (C) x = 2 x = 2. (D) x = -2 x = −2 and x = 2 x = 2. (E) x = -4 x = −4 and x = 2 x = 2. Answer (C) Explanation : The function f (x) = \frac {x^2 - 4x} {x - 2} f (x) = x−2x2−4x is undefined when the denominator x - 2 x − 2 equals zero. Therefore, the function is undefined at x = 2 x = 2.

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  5. 16 de abr. de 2024 · Join Teachoo Black. Example 20 Find the derivative of f (x) from the first principle, where f (x) is (i) sin x + cos x Given f (x) = sin x + cos x We need to find Derivative of f (x) We know that f’ (x) = lim┬ (h→0) 𝑓⁡〖 (𝑥 + ℎ) − 𝑓 (𝑥)〗/ℎ Here, f (x) = sin x + cos x f (x + h) = sin (x + h) + cos.

  6. 16 de abr. de 2024 · Example 7 Is the function defined by f (x) = |x|, a continuous function? f (x) = |𝑥| = { (−𝑥, 𝑥<0@𝑥, 𝑥≥0)┤ Since we need to find continuity at of the function We check continuity for different values of x When x = 0 When x < 0 When x > 0Case 1 : When x = 0 f (x) is continuous at 𝑥 =0 if L.H.L = R.H.L = 𝑓 (0 ...

  7. 16 de abr. de 2024 · Ex 3.2, 13 If F (x) = [ 8 (cos⁡𝑥&〖−sin〗⁡𝑥&0@sin⁡𝑥&cos⁡𝑥&0@0&0&1)] , Show that F (x) F (y) = F (x + y) We need to show F (x) F (y) = F (x + y) Solving L.H.S. Given F (x) = [ 8 (cos⁡𝑥&〖−sin〗⁡𝑥&0@sin⁡𝑥&cos⁡𝑥&0@0&0&1)] Finding F (y) Replacing x by y in F (x) F (y) = [ 8 (𝐜𝒐𝒔⁡𝒚&〖− ...