ing the limit definition of derivative, find the third derivative of g, given g'(x) = 2-√√x+1

Q: Solve the integral below using integration by part. [(2x - 3) 3) e* dx

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Q: Dividing the polynomial P(x) by x-1 yields a quotient Q(x) and a remainder of 4.  If Q(-1)=3, Find…

A: P(x) =Q(x) (x-c) + R(x)when the factor is (x-1)R(x)=4P(x)=Q(x) (x-1)+4P(1) =0 +4P(1) =4

Q: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. 2 YA a. f*…

A: solution is given below..

Q: Find the average value fave of f(x) = f(c) = fave. fave = C = between 1 and 1, then find a number c…

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Q: Assume P and Q are points on the graph of the function y = f(x). If the a-coordinates of P and are a…

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Q: Consider the function f that is continuous on the interval [-5, 5] and for which ff(x) dx = 4.…

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Q: Question You work at a farm that wants to build three identical rectangular corrals in a row against…

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Q: In the triangle below, BA=u and BF=v. Express each of the following in terms of u and v. a) CD b)…

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Q: Find the area of the region under the graph of f on [a, b]. f(x) = x² - 6x + 13; [−1, 2]

A: To find the area of the region under the graph of f(x)=x2-6x+12 on the interval [-1,2].

Q: Let f(x,y) = 4(x + 1)²(y - 1) - y² - 8x²-16x + 2y - 18 (i) Find the sum of all x- coordinates of the…

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Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: The proper transformation for sin²x to make the f sin²x dx readily integrable is {A} 1- cos²x {C}(1-…

A: Given the query is to find the correct option of integral.

Q: Find the area of the surface x²-6y-2z=0 that lies above the triangle bounded by the lines x = 4, y =…

A: Surface Area :        Surface Area = ∫∫R 1+zx2+zy2 dA

Q: analyze and trace the given curve y = 2x3 + 3x2 - 12x + 7

A: Given:

Q: m(x) be the slope of the tangent line to the curve y = 2x3-6x² + 3x at the point (x, y). Find the…

A: Slope of tangent line is dy/dx

Q: Create Representations to Communicate Math find the total surface area of each prism. 1. 2. 6 f 29…

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Q: Find the surface area generated by revolving one arc (first quadrant) of y = cos x about the x-axis.…

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Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t = 1|3

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Q: The f e²x +e-2x e2x-e-2x dx is -2x1 {A}={In 2x te e e2x-e-2x + C 2x {B} In|e²x −e-²x | + C {C} -2…

A: To solve the given integral using substitution.

Q: Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find…

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Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: We have to find the maximum profit.

Q: A company plans to manufacture rectangular boxes with no top that have volume 12 cubic feet. The…

A: Given problem:- A company plans to manufacture rectangular boxes with no top that have volume 12…

Q: Find the future value of a $20, 000 annual income stream if it is invested immediately as it is…

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Q: Find the derivative of the vector function r(t) = (tsin t, t^2 , t cost)

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Q: 2000, the population of a city was 71,000. The population had grown to 100,000 by 2011. If the…

A: Given query is to find the population in 2026.

Q: The cos³dy is {A}-sin+sin³+C 3 3 3 4 {B} sin¹-sin³+ C 3 4 3 4y (C)-sin-sin³+C {D}sin+sin³+ C

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Q: 3. Graph the hyperbola, put the equation into standard form and identify the asymptotes, vertices,…

A: The given hyperbola equation,      9x2-4y2-36x+8y-4=0

Q: An equation of a conic is 5 r = 3+2 sin 0 Identify the conic, find the eccentricity, write an…

A: A conic section with a focus at the origin, eccentricity e, and directrix at x=±p has polar…

Q: 4 Water drips into a conical container, which is orientated point downwards, at a rate of 100…

A: This is a problem related to mensuration. Based on the formula for volume of cone and derivative…

Q: Question Consider the function f(x) below. Over what open interval(s) is the function increasing and…

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Q: 6) The variables x and y satisfy the differential equation X = y(1-2x²), dx and it is given that y =…

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Q: d d Calculate[ri(t) r₂(t)] and[r₁(t) × r₂(t)] first by differentiating dt the product directly and…

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Q: Find the area of the region bound above by y = 2cosx and below by y = secx,-π/4 ≤ x ≤ 1/4.

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Q: Use one of the following three formulas for the area of the region enclosed by C 1 fxdy = f - ydx =…

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Q: Use the formula k(t) k(t) = ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) = t²i+t³j to find k(t).

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Q: Use a graph to estimate the coordinates of the lowest point on the curve x = t³ - 31, y = 1² +1+1.…

A: Consider the parametric equation x=t3-3ty=t2+t+1 Sketch of the parametric equations is shown below.

Q: construction company will be panalized each day of delay in construction for bridge. The penalty…

A: Given the query is to find the maximum possivle days for delaying.

Q: Ⓒ Given SS² +8 dy dx. Reverse the order of in tegration and evaluate. Draw the region.

A: In the given problem first we draw the region then reverse the order of integration and after that…

Q: The eigenvalues of the matrix 139 - 84 240 145 (a) Find an eigenvector corresponding to X₁ = 1 X1 =…

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Q: Find T, N and B for the curve F(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t -0 Give your answers…

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Q: Find the indefinite integral. Solution in handwritten b. f(x+1)√2- xdx

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Q: ∞ n=1 (n+1)(3² − 1)¹ 32n

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Find the indefinite integral. Solution in handwritten. 1. secy (tany - sec y ) dy

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Q: 6. What is the integral that describes the enclosed region between y = 4x - x² and the x - axis ? A.…

A: Given problem:-

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given problem:- Find the domain of r(t) and the value of r(t0)  r(t) = cos(πt)i - ln(t)j + √(t -…

Q: Find the arc length L of the graph of r(t). r(t) = 1³ i + 1 j + = √61² k, 3≤1≤7

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Q: Find the Definite Integral Exactly and use Desmos to explain what you just found. -2 3. S²(x² - 3*)…

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Q: * Find the derivative lic F (+) = (+³-2+ +1) (2+²

A: Given query is to find the derivative of the expression.