Sketch the triangle with vertices O, P = (4, 0, 4) and Q = (6, 7,0) and compute its area using cross products. Area=

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Q: If F(x) = f(g(x)), where f(-4)= 3, f'(-4)= 8, f'(5) = 5, g(5) = -4, and g'(5) = 6, find F'(5).

A: F(x)=f(g(x))where f(−4)=3,f′(−4)=8,f′(5)=5,g(5)=−4, and g′(5)=6,

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Q: 1. Evaluate the integrals by using the integration by parts. (b) f(lnx)³ dx (a) [x² cos x dx (c) S x…

A: Here we need to use Integration by parts for those integration solutions.

Q: 767-72. Applying the Intermediate Value Theorem a. Use the Intermediate Value Theorem to show that…

A: let f(x)=

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A: Application of algebra

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Q: r(t) = (15 sin(5t), 2√14 cos(5t), 13 cos (5t)). a. Find the arc length function for (t). s(t) = 75t…

A: Given that ,

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Q: Use logarithmic differentiation to find the derivative of the function. y = (x³ + 2)²(x³ + 4)4 y'(x)…

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Q: Question What value(s) of 8 are an appropriate choice when proving the following limit? lim (√√8x32)…

A: We have to find the delta using the epsilon-delta definition of a limit.

Q: Part D. Problem Solving: (1) Predicting the Cost of a Compact Car. In 2010, the cost of a compact…

A: Solution-Given in 2010, the cost of a compact car averaged $8000, In 2013, the cost of a compact car…

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A: Given, the graph of the function y=f(x) (figure), we find the graph of the transformed functionsa.…

Q: Consider the indefinite integral [e7²+5 A. This can be transformed into a basic integral by letting…

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Q: (2) Let f(x) = -3 sin(x+2). (c) And then determine the domain and range of f(x).

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Q: Evaluate the limit lim x →∞ (8 - x)(6 + 7x) (310x) (7 + 4x)

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Q: 9-11. Let F(x) = f(x) + g(x), G(x) = f(x) - g(x), and H(x) = 3f(x) + 2g(x), where the graphs of f…

A: Note:As per our guidelines we are supposed to answer only one question If there are multiple…

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Q: Write an inequality to describe the region. The solid cylinder that lies on it between the plane z=5…

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Q: Find the derivative of the function. f(x) = x(4x - 7)³ f'(x) =

A: Since you have asked multiple questions. We will solve the first question for you. If you want any…

Q: 1. a) Compute the point of intersection of the two lines ₁ (t) = (2+ t, 1 + 2t, 5 + 3t) and r₂(t) =…

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Q: 10. (opts) a) Use the rules of differentiation (Not the limit definition) to find the derivative.…

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Q: Find all numbers b such that the average value of f(x) = 3 + 10x - 6x2 on the interval [0, b] is…

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Q: 4 Use a graphing calculator to sketch the graph of f(x) = evaluate the following limits. a) lim f(x)…

A: as per our guidelines we can answer only 3 sub parts of a given question so kindly repost the…

Q: Let f(x) = ex/(x + 4) 2 X x² - 36

A: f(x)=ex/(x+4)x2−36

Q: Evaluate the limit: - 7x - 21 lim x-3 x² - x - 12 =

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Q: Let F(x)=x² (a) Estimate the values of f(0), (2), P(1), (2), and F(3) by zooming in on the graph of…

A: Solution is following in explanation step.

Q: Problems 10-12, Use the given zero to find the remaining zeros of each function. 10. f(x) = x³2x²…

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Q: Find dx dy by implicit differentiation. dx y cos(x) = 3x² + 4y² 11

A: consider the given function.

Q: (3) Let R(x) = 2 +3- (c) Evaluate the function when x = -6, -5, -4.5, -3, -0.5, 1.5, 4, 6;

A: To evaluate the function at given values of x

Q: Let f(x) = Determine the following: lim f(x) x →4 Can be found, lim___ƒ(x) = x →4¯ lim x→ 4+ 2 x -…

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Q: 78-81. Derivatives from a graph Let F = f + g and G = 3f - g, where the graphs of f and g are shown…

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Q: ts) Graph the following function f(x) = (-x if x < -2 x² if-2 ≤ x < 2 (3 if x ≥ 2

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Q: Give a geometric description of the set of points in space whose coordinates satisfy the given pair…

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Q: Q2. Find area of the region in 2D plane (x,y) given by: (it is sufficient to provide an expression…

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Q: lim h→0 lim h→0 lim h→0 lim h→0 −(2+h)² +3h+4 2 -(2+h)² + 10 2 -(2+h)² +3h+4 h -(2+ h)² + 10 h

A: We are to evaluate the given limits.

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Q: Test the series below for convergence using the ratio test. Σ n 1.1" The limit of the ratio test…

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Q: The solution to the Initial value problem x" + 2x + 17x = 4 cos(4t), x(0) = 0, r'(0) = 0 is the sum…

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