Let f(x) = 2 3 x3 + x2 − 12x + 1. Find the values of x for which the following are satisfied. (Enter your answers as comma-separated lists.)

Q: Compute the distance from the point (3, 0, -1) to the line containing the points (1,0,−4) and (1,…

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Q: Test the series below for convergence using the ratio test. n+1 2³n+1 n=1 The limit of the ratio…

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Q: 5. Let f: Z→ Z defined by f(x) = 4x² - 3. Determine the following. a) Domain d) Is f one-one? b)…

A: Since you asked multiple sub parts questions, according to our policy we can solve only first three…

Q: Find f''(x). f(x)=2x-7

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Q: A = (x EZ: xis even} B = (x E Z: xis a prime number} D = (5,7,8,12,13,15) Select the set…

A: Given: To find the set .

Q: Olim x→1 1 x+1 x 1 - 1|2

A: Explaination of the answer is as follows

Q: Find the volume of the parallelepiped (box) determined by u, v, and w. u = 2i + 3j, v=4i-3j + 3k, w…

A: To find the volume of the parallelpiped (box) determined by thefollowing vectors.

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y =…

A: given curve We know that area of surface obtained by rotating y=f(x) from x=a to x=b  about x-axis…

Q: Find the angle between the vectors. u= √√2i - 3j, v=√√2i+j-3k The angle between the vectors is 0 =…

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Q: Given s(t)=5t+20, where s(t) is in miles and t is in hours, find each of the following. a) v(t) b)…

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Q: R 360 N a) The supporting cables AB and AC are oriented so that the components of the 360-N force…

A: We have to determine angles and components of force along cables AB and AC.

Q: Find product in compuex plane [ 3 ( (os (4) + (Sin (#)) [ 5 (cos ( 2 ) +isin (1/4))) X

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Q: Consider the curve parametrized by x = t4 + 1 and y = e²t - 1. dy a) Find dx dy da b) Find d²y/dx²…

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Q: (2) The population of the world in 1995 was about 5.7 billion, and the estimated relative growth…

A: The exponential growth model Population at time tInitial population relative growth ratetime in…

Q: Find an equation of the tangent line to the graph at the given point. (The graph is called a Witch…

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Q: Let f(x): = x² and compute the Riemann sum of f over the interval [4, 6], choosing the…

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Q: Consider an object moving along a line with the given velocity v and initial position. v(t)=2 sin 4t…

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Q: QUESTION 3 Find the slope of the tangent line to the graph of y = x2 at (8/7, 64/49) and write the…

A: Finding the slope of the tangent line to  the graph y = x2 at (8/7, 64/49)

Q: 3) Find the volume of the solid of revolution formed by rotating about the x-axis each region…

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Q: Consider the curve C parametrized by x = cos (8t) and y = sin (8t), for 0 ≤ t ≤ π/8 and traversed by…

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Q: Write the equations of all asymptotes for each rational function. Use limits! 1. f(x) = 3x²-1 x-2 2.…

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Q: A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a…

A: The given equation is,The average velocity on the interval [2,2.01] is given by,

Q: Orthogonal Matrix Determine whether matrix A given below is an orthogonal matrix 0.8 0.6 00 -0.6 0.8…

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Q: Let C be the curve y = 5x³ for 0 ≤ x ≤ 1.2. 8- 7+ 6+ 5 4 3- 2 1 0.5 Q Find the surface area of…

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Q: Suppose $500 is invested in an account at an annual interest rate of r = 8.2%, compounded…

A: Given, $500 invested in an account.interest rate=r= 8.2% time= 15yearsformula for compounding…

Q: Consider the following series. (-3)*¹ ∞0 n=1 Does this series converge or diverge? O diverges…

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Q: y= 3x-2 2x+3 y"=0

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Q: For r(t) = (3sint)i + (3cost)j + 4k Determine: 1. The unit tangent vector (T). 2. Principal unit…

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Q: For what numbers c are 4ci – 3j and 5ci + 2j a) parallel? b) orthogonal?

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Q: Use the comparison test (sometimes called the direct comparison test) to determine if the series n=1…

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Q: 2. Find all the zeros of P(x)=x²-21x² - 100 given that -2i is a zero.

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Q: Consider the following function. Use a graphing utility to confirm your answers for parts (a)…

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Q: Find the volume of the parallelepiped (box) determined by u, v, and w. u = i +3j, v=4i-2j + 3k, w =…

A: u=i+3jv=4i-2j+3Kw=3i+3kDetermine the volume of parallelepipe

Q: Find the gradient of the function at the given point. Function f(x, y, z)=√√√√x² + y² + z² Vf(7, 3,…

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Q: A company introduces a new product for which the number of units sold S is given by the equation…

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Q: The graph of a function is given to the right. Use the graph to find each of the following. a. The…

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Q: lim tan 4x X-70 3X = نگامی که

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Q: 1 2 Let A = and let f(x) = 2x² - 4x + 5, g(x) x² + 2x + 1. Find f(A) and 4 -3 g(A). Remark. In the…

A: Given,.To calculate f(A) and g(A). This can be done as follows:

Q: The primitive of the function f(x)=x√√2+x² whose graph passes throu the point P=(√2,0) is: (a) =—=…

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Q: 10. Using the precise definition of a limit, with and 8, prove lim 2x² - 4x + 1 = -1. x-1

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Q: Find the gradient of the function at the given point. f(x, y) = 3x + 4y² + 2, (3, 1) Vf(3, 1) = = X

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Q: (2) Let f(x) = -3 sin (x + 1). (b) Find the five special points on the graph of y = f(x) in the…

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Q: Compute the right-hand and left-hand derivatives as limits and check whether the function is…

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Q: (1) Let P(z) = 21²-71³ +1² +7x-3. (a) Describe the end behavior of the graph for y= P(z) when z→…

A: We have given a function and we have to find end behavior, x and y intercepts, turn points and then…

Q: (i) lim x-2 √1+ 4x - 3 2 x

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Q: Step 2: Solve for Ay: Ay = f(x+ Ax)-y Ay = f(x + Ax)-f(x)

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Q: (b) [a²e -2x dx ²e-2

A: Given data:The given integration is .we know,

Q: Draw the graph and answer the following: f(x)√(x₁ - 1EXCO or OLX ≤₁ X, X=0 Lo, x 1 a) at what points…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Use calculus to derive the volume of the unit sphere.

A: Use calculus to derive the volume of the unit sphere.