What is the area of the region bounded above by y = -x- + 8 and below by y = x? 54 $2 14 1 23 4 5 64 3. 32 22 3. 11

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Q: Consider the following. g(x) = (5x – x³) h(x) = (3x + 4) f(x) = (5x – x³)(3x + 4) Find g'(x) and…

A: gx=5x-x3hx=3x+4fx=5x-x33x+4

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Q: Solve the equation: (2r – xy? – 2y + 3)dx – (x²y + 2x)dy = 0 x4 – 2ry? – 4xy + 6x = c O x* - x²y² –…

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Q: 1. If f(x)=1/x, which of the following is the simplified form of the difference quotient? * -h -1…

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Q: Solve the exponential equation. Express irrational solutions in exact form. (7/5) ^ x = 9 ^ (1 - x)

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A: We need to integrate given function.

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A: We need to find if the function is continuous or not in given interval.

Q: Given the function below find the value of f(-5). * [2x² + 1 if x -5 33 NONE OF THESE -78/25 O 51…

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Q: Find an equation of the plane through (0, -9, – 1) that is perpendicular to the line x - 2 = 3t, y +…

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Q: Find the direction cosines and angles of u and show that cos? a + cos2 B + cos2 y = 1. (Round your…

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Q: Find the derivative of the function described. (Rx5) 4х-2 5. у 3 3x+4

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Q: Find the volume of the solid bounded by the graphs of the given equations.   z = xy,    z = 0,…

A: Given problem:- Find the volume of the solid bounded by the graphs of the given equations.   z = xy,…

Q: Find u v, u·u, ||v||², (u · v)v, and u · (3v). (5, -2, 4), v = (0, 7, 5) U = (a) u V (b) (c) ||v||?…

A: The given vectors,  u=5,-2,4, v=0,7,5

Q: nin m Find the distance between the point and the line given by the set of parametric equations.…

A: This question is based on 3-d line.

Q: Many statistics courses cover a topic called multiple regression. This provides a means to predict…

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Q: valuate lim v9x² – 5x + 3x

A: Given: limx→ -∞ 9x2-5x+3x

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = - 2…

A: This is a problem related to function calculation. Based on the graph we can find out the interval…

Q: Given the graph of the function below. Find the limit of the function as x approaches 5. * (3, 4)…

A: From the given graph, we have to find the limit at x=5

Q: Let C = (1,–3, 2) and D = (-1, 2, – 3, ). Find the following. (a) The cosine of the angle between D…

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Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

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Q: dy 3) Determine the of : In (ху?) %3D х у dx

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Q: Determine if the given sequence converges or diverges. If it converges, what is its limit? n+11 (d)…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: Solve the area of the surface of the revolution generated by revolving the arc of the curve, x= y³…

A: A detailed solution is given below.

Q: Homogeneous or not? State the degree of function if homogeneous. x^3-xy+y^3

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Q: Let f(r) = r³ – 3x² + 4. Using the Mean Value Theorem, determine the value of c € (0, 3) such that…

A: A detailed solution is given below.

Q: Consider the following. u = (2, -1, 0) v = (-2, 3, 0) Find u x v. Determine if u x v is orthogonal…

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Q: List the first 5 terms of the sequence. 1 22 3n 3n3 32 3n n2 3n (b) -2)n+1 + 3" (a) an =

A: For (a), Given: Now, an=13n3+223n3+323n3+...+n63n3   =13n31+22+32+...+n2   =n+1n+22n+363n3…

Q: Let <0,4,27 < 3, 0 , 1) What is the having the same direction B- ZA + c ? unit vector as

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Q: (a) Graph the equations in the system. (b) Solve the system by using the substitution method. (x+3)°…

A: Using substitution method.

Q: Medicine The graph shows the estimated number of milligrams of a pain medication M in the…

A: Given: The graph shows the estimated number of milligrams of a pain medication M in the bloodstream…

Q: 13 For the sequence an = n +1' its first term is its second term is its third term is its fourth…

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Q: Consider the following equation and point. f(x) = a (3, -1) x - 4 Find an equation of the tangent…

A: First we have to calculate slope of the given function to calculate equation of tangent

Q: Use the formula k(t) : ||r(t) × r"(t|| to find k(t). r(t) = 11 cos(t)i+11 sin(t)j + 6tk K(t) =

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Q: Consider the following. u = 9i + 5j v = -8i + j + 6k Find u x v. 1li – 54j + 49k Determine if u x v…

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Q: /3x+10 4 Evaluate lim x- 2- x2- 4x +4 А. 1 В. 3/8 D. -00 E. None of these C.0 B O D E O A

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Q: se the General Power Rule to find the derivative of the f y = 124x2 + 5

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Q: Question For the function given below, which statements concerning Rolle's theorem are true? f(x) =…

A: f(x)=x3-16x+2    ;  [0,4]

Q: What can be concluded when integral test is applied to the following series? 1 (2n + 1)3 Select one:…

A: The given series is: ∑n=3∞1(2n+1)3 Let, an=1(2n+1)3, n≥3

Q: 11T If 0 = then 6 sin(0) = cos(0) Give exact values. No decimals allowed!

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Q: 7) Determine the particular solution to the differential equation y 3x-2 that passes through the…

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Q: Find the direction cosines and angles of u and show that cos a + cos B + cos? y = 1. (Round your…

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Q: 5x2 + x + 16 dx x3 + 4x 9)

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Q: Find the following. = (3, 5) U = %3D (a) ||u|| (b) ||v|| (c) ||u + v||

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Q: I just need help solving this integral

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Q: 1.(a) Do there exist integers a, b, c such that gcd(a, b) = 30, gcd(b, c) = 24, gcd(a, c) = 54?…

A: (1) gcda,b=30=2×3×5  ...(1)gcdb, c=24=23×3    ...(2)gcda,c=54=2×33     ...(3)

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: Solution is given below: