Identify the vertex of: f(x) = 3(x - 5)² + 1/2 O (-15) O (5) O (-1/52,7) O (5,-)

Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…

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Q: For f(x)= x+4 and g(x) = 2 x + 6, find (gf) (x). O 2x² +24 O 2x² +14x+24 O 2x²+14x+10 2x² +10

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Q: Give the derivative formula for the function. f(x) =  6x2−3                 3x

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Q: Suppose f(x) = x³ − 6x² − 63x + 10. Find the absolute extrema of f on each of the following…

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Q: Given the function f(x) = −2x² Find the difference quotient f(x+h)-f(x) h Find f'(x) by determining…

A: Please see the below picture for detailed solution.

Q: Use the graph of f" shown below and the letters A, B, C, and D representing x values to answer the…

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Q: tion about the origin. hat is the 13. Let T: R2 R2 be the linear transformation such that T(e₁) and…

A: Please see the below picture for detailed solution.

Q: For each of the following integrals find an appropriate trigonometric substitution of the form x =…

A: We have to find the appropriate substitution.

Q: QUESTION 1 If f(x)=x and g(x)=k-x are orthogonal over [0,1]. Then k = ..... O 1 O O N/W W/A W/ W/N…

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Q: Determine the open intervals on which the graph is concave up or concave down. If there is more than…

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined points, take…

Q: Find the component forms of v+w and v- w in 2-space, given that ㅠ ||v|| = 7, ||w|| = 3, v makes an…

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Q: Write a mathematical model for the following statement. Use k as the constant of variation. s varies…

A: We have given a statement  s varies directly as square of t sαt2 s=kt2

Q: r = ep 1 - ecose

A: Given    r=ep1-ecosθ

Q: The graph of a function f and a tangent line to f at the point B are shown in the figure below.…

A: Given: The graph of a function f and a tangent line to f at point B are shown in the figure below.

Q: Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values…

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Q: Find the missing value. y varies inversely as x. y = 10 when x = 5. Find y when x = 2. 3 O y = 10 O…

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Q: By the Horizontal Line Test, the graph below represents a one-to-one function. - O True 111 O False

A: Horizontal line test - If a horizontal line intersect the graph of a function more than once…

Q: Find the area under the curve y = sin(t) area = cos(t) between t = 0 and t = π/2. Enter diverges if…

A: The region bounded by the curve y=costsint between t=0 and t=π2. We have to find the area of the…

Q: For each of the following integrals, decide if it is a proper integral or improper integral. Justify…

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Q: Calculate line integral 9 F-dr, where F(x, y) = (x² + y, 3x −y) and C is the positively oriented…

A: To calculate the line integral of the vector field F along the boundary curve C, we need to…

Q: The following functions are inverses of each other. f(x) = 3x - 7 and g(x) = x+3

A: given function f(x)=3x-7 and g(x)=x+73

Q: 20 Let f(x) = 3x + Then the equation of the tangent line to the graph of f(x) at the point (2,11) is…

A: The given function is fx=3x+20x2 and the point is 2,11.   The objective is to find the equation of…

Q: The rate of change in value V'(t) of a commodities index per day is given by the following equation…

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Q: Consider the following series. 00 n = 1 1 x0.6 Evaluate the following. [ Use the Integral Test to…

A: We want to find the convergence of the given series of using integral test.

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: After his graduation, a Wilfrid Laurier University student departed Earth to find work on Mars. A…

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Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z)= In (3z-2x³-2y²-2) b.…

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Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

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Q: Given the series ∞ 5″ Σ n=1 n an+1 an (Express numbers in exact form. Use symbolic notation and…

A: given  ∑n=1∞5nnthere for  an=5nn

Q: 15. Consider a box with dimensions 3 cm x 5 cm x 11 cm. If all of its dimensions are increased by x…

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Q: Evaluate the definite integral 3x³-4x² x² -dx

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Q: it exists) integral (if it exists) Find the indicated integral (if ·∞ e4x e8x + 1 dx =

A: The given integral is e4x/[e8x+1], limit from -infinity to infinity.

Q: 10. S 1 x²+2x dx

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Q: Find u and v if u+6v = 6i- k and 3u-v=i+j+ k. NOTE: Enter the exact answers in terms of i, j and k.…

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Q: substitution method [ sin³ (7) cos (1) da dx 3

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Q: 18. Sőt dx √1-x²

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Q: A solid is formed by rotating the region in the first quadrant of the xy-plane y = e2 + 1 and x =…

A: We need to find out the volume of revolution.

Q: Consider the function f(x) = 4x² - 4x4. (a) Find all critical numbers c of f. C = (b) f is concave…

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Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0 ≤ 0 <…

A: Use the concept of derivative of polar equation and solve for horizontal and vertical tangents.

Q: Suppose f(x) = xe-³x, 0≤x≤ 2. Use the Closed Interval Method to find points at which the absolute…

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Q: Find the smallest positive root of the equation ex cos(x) 201 Correct to 4-decimal Places, take Xozl…

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Q: Assume C is a circle centered at the origin, oriented counterclockwise, that encloses disk R in the…

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Q: Evaluate the following summations. (a) _ Σ = 4k2 + 5k – 3 n-1 k=1 (b) Σ+1 i=1 Σ=&ij

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Q: 1+csc(x³) 1-cot (⁹)

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Q: 2. Prove that d [(2x+1)³] (2x+1)³(4x-19) (x-3)² dx = Then, -5 (2x+1)(8x-38) 3(x-3)² dx.

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Q: Use the piecewise defined function below to answer the questions. 2 x 0 f(x) = √x³. 5 1/x

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Q: Evaluate the integral. 5x 2x dx fate con in die 049 O ㅇ [sin 2x + cos2x) + C 12 sin 2x-5 cos 2x) + C…

A: We need to solve the following integral I = ∫e5xcos2xdx

Q: Maximizing Profits A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of…

A: We first find the profit function.  P(x)=R(x)-C(x)P(x)=px-C(x)P(x)=(10 − 0.0003x)x-700 + 8x +…

Q: Simplify. Y -2x -1 yx ° -2yx 6x² - 5x [6²² 8yx 6x² - 5x [62³% 2yx 6x² - 5x 162² [152² 2yx 15x²–5x…

A: It's simply a matrix multiplication. Use the raw into column multiplication of matrices.

Q: Find exactly the vector oppositely directed to v = (3) and half the length of V. i i

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