The following are the left, right, trapezoid, and midpoint approximations (not necessarily in that order) to che definite integral f(x)dx, where f'(x)<0 and f"(x)>0:

Q: Given the function f(x, y, z) = (sinx)(cosy)(ln z), find the total derivative with respect to x,…

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Q: How many comparisons of lists using Algorithm are required to merge these pairs 10? a) 1, 3, 5, 7,…

A: Algorithm 10 is a bit vague without a specific description, but typically, when merging two sorted…

Q: Find the equation of the tangent line to f at x = a. f (x) = x2 + x, a = 1

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Q: 3. Use the second derivative test to find the local extrema of f(x) = cos x + sin x on the interval…

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Q: 2. Given the function -a Show that

A: Note :-  Since you have asked multiple question As per our policy, we will solve the first question…

Q: A. Find the derivative of this function: h(x) = the definite integral from 0 to x of…

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Q: d -(tan²(x) - dx 1 Prove that : 1+x*

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Q: 42. y=+on [1/2,2] 6

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Q: . Use the forward-difference formula to approximate the derivative of f(x)= Inx at x, =1.9 using…

A: Forward Difference: For small values of h, the difference quotient can be used to approximate with…

Q: 1. Applying the definition of derivative, a. find dy/dx in each of the following: 1 a. 1] y = - x² –…

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Q: Consider the integral (x) dx where f(x) is a smooth continuous curve. One or more of the following…

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Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

Q: Which of the following has a derivative of * dy = 32.x + 24? dx

A: The derivative dydx is given by dydx = 32x + 24                          ........(1)

Q: If f(x, y, z) = 7xy²z³ + arcsin(x√z), find fx [Hint: Which order of differentiation is easiest?]…

A: If fx, y, z=7xy2z3+arcsinxz, then to find fxzy.