Find the exact length of the curve. y = ² ²x³/2, 3 0≤x≤6

Q: nd the maximum rate of change of f(s, t) = test at the point (0, -3).

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Q: 2x+2x+3 Consider the function (a) To use a limit and find its horizontal asymptote what must be done…

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Q: Give the function f(x)=x State what it means. Evaluate the one-sided limit: lim x₁+f(x).

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Q: Find all solutions of the elation in the interval [0, 2π). cos 0-1=-1 Write your answer in radians…

A: The equation in the interval [0,2 pi).cos theta - 1 = - 1 Add 1 both sides, we get theta =0

Q: Find the equation of the tangent line at the indicated point. R(2)=log, (222-79), z=8

A: R(z)=log7⁡(2z2−79),z=8R′(z)=ddzlog7⁡(2z2−79)Using the Chain…

Q: The derivative of the [Select] of two functions is the first times the derivative of the second,…

A: Consider that have two functions and . The product rule states that:where:- and are the two…

Q: Let us model the number of automobile sales in a developing country as N(t) 158,000…

A: a) 22899 cars at 2010b) 122566 cars at 2020c) cars sales stabilize at 158000 cars.Explanation:

Q: Tutorial Exercise Find the arc length function for the curve y=2x3/2 with starting point Po(16,…

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Q: Evaluate the following surface integrals [ F. ds. (a) F(x, y, z) = (x, y, z) and S is the part of…

A: The solution is given below please refer to the solution  and if you have any doubt with regards to…

Q: The shaded region shown below is bounded by the functions f, of, x, equals, minus, 3, x, squared,…

A: Given that the region is bounded by the curves and  and the x-axis and the y-axis.

Q: C. Find the equation of the plane that passes through the points A(1,-1,1), B(1,2,0) and C(0,1,-1)

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Q: Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator…

A: x=−1,0,1y=−1Explanation:Given the equation,y=x2−x42+x4​ Solving for horizontal and vertical…

Q: A race car is traveling at a speed v in km/h. When the brakes are applied the distance d (in metres)…

A: d= 0.4v2+3vWhere d is in metersWe have to find instantaneous rate of change of stopping distance…

Q: Evaluate the integral 0 [(6te³¹²) i + (3e¯71) j + (1) k] dt.

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Q: Consider the definite integral Cx3 dx 0 How many partitions would be needed to approximate this…

A: The given integral is The error bounds for the midpoint rule If  and  be the error in the mid point…

Q: Let the function: f: R → (0, ∞), f (x) = ex+3 Show that f is one-to-one correspondence (bijective)…

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Q: Convert the Cartesian coordinate (-2,3) to polar coordinates, 0 ≤ 0 < 2π r = 0 =

A: r=(​13)θ=π−tan−123​Explanation:For any query with the solution, please ask in the comment box.

Q: - The Parametric equation of the line that passes through the point A(1, 1, 1) and parallel to the…

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Q: Differentiate the function. 이 y=(3x-2) (4-x)4 dy 口 dx

A: To differentiate the following function.

Q: Calculus 1 Question. Please help   Thank you

A: Ans : dxdy​=6cos6xExplanation:Explanation:

Q: 8) Write the expression -3sinx + 4cosx in the form ksin(x + a) for 0 < a < 2. Round a to three…

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Q: On what interval(s) is the function f(x) = x - 4x³ both decreasing and concave up? (Enter your…

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Q: Please help with Calculus 1 Problem. Thank you.

A: Please refer below to get your solution.Explanation:Sol)

Q: The diagram below illustrates the number of moose (red curve) and wolves (blue curve) between 1960…

A: The diagram below illustrates the number of moose (red curve) and wolves (blue curve) between 1960…

Q: Find the directional derivative of the function f(x, y, z) = √xyz at the point (3,2, 6) in the…

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Q: f(x, y, z) = √√√x²+ y² + z² ZA x E 25

A: f(x,y,z)=x2+y2+z2From the figureRegion is bounded by two quarter spheres…

Q: Find the interval(s) where f"(x) > 0. (Enter your answer using interval notation.) Find the…

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Q: rientation toward the origin. √s F. ds =

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Q: 4. Let A, B and C be subsets of the universal set U. Draw the Venn diagram for (CUB)N(Ā-C). U C B

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Q: Match the graph of each function in A through D with the graph of its contour map in 1 through 4…

A: Close together contours indicate a steep slope, wall or cliff..

Q: See the function in the image uploaded. Answer a) a) To use a limit and find its horizontal…

A: The objective of the question is to find the horizontal asymptote of the given function y = (2x^2 +…

Q: Use Linear Approximation to estimate Af = f (9.02) - f(9) for f(x) = x4. (Use decimal notation. Give…

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Q: The equation r(t)=(12 sin t) i+ (4 cos t) j +(8t) k is the position of a particle in space at time…

A: The equation  is the position in space in time . To find the particle's velocity and acceleration…

Q: If f'(x)=0 for all *, then a) f(x)=(x) for every x₁ x₂ c) f(x)>(x) for every x₁>x₂ d) f(x)>(x) for…

A: If  then which option is correct .

Q: 7 63 tan (a+b); cosa for a in Quadrant III and sinẞ: for ẞ in Quadrant IV. 25 65 tan (a+B) Find the…

A: tan(α+β)=−162457​Explanation:

Q: The center A and the radius R of the following sphere x² + y² + z² - 2x - 2y2z1 are Ignore "Give…

A: The given sphere is, , we have to find the radius and center of the sphere.Standard form of a sphere…

Q: Find the angle of intersection, in radians on the domain 0 <t≤, to two decimal places.

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Q: (a) Evaluate the surface integral ff z² dS, where S is the upper half of the sphere x² + y² + z² =…

A: For part (a), the surface integral evaluates to(−332π​). For part (b), the surface integral…

Q: Give the probability distribution for the indicated random variable. (Enter your probabilities as…

A: The probability distribution of X is shown below.x23456789101112P(X=x) 1/36 2/363/36 4/36  5/36 6/36…

Q: Consider the function x²+2x-1 if x ≤ -1 f(x) = 3/8x 2x+4 3 if − 1 1 (a) To determine whether f is…

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Q: Find the slope of the tangent line to the curve below at the point (7,7 4x+3y+ √3xy =…

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Q: Use the equations OF JF дг дх Əz ду and дх OF ду OF dz Əz Əz მz to find and дх ду ez = 6xyz II || მz…

A: ​∂x∂z​=ez−6xy6yz​∂y∂z​=e2−6xy6xz​​Explanation:Step 1:​Given an implicit function.ez=6xyzTo find: The…

Q: dy Use implicit differentiation to find without first solving for y. dx -16x³ + 4x16y+y₁ = 77

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Q: Let f(x)=xex. (Round all answers to four decimal places, if necessary.) (a) Find the interval(s)…

A: The given function is As we knowThe function concaves up when The function concaves down when The…

Q: Use a half-an le formula to find the exact value of tan 105°. tan 105° = 0 G

A: .

Q: find the length of the curve  y = 2/3(x^2 +1)^(3/2) from x=3 to x=6

A: The length or arc length of the given curve is 129 units.Explanation:

Q: Write out the first five terms of the sequence with, [(1-8)] determine whether the sequence…

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Q: Evaluate the following integrals using partial fraction decomposition, when applicable

A: If you've any doubt comment below-Explanation:

Q: Let f(x, y, z) = x4y²+ z² and x = = st³, y = s²t³, and z = st. (a) Calculate the primary derivatives…

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Q: Find the linear approximation to the equation f(x,y) = 2√ xy at the point (2,8,4), and use it to…

A: Therefore, the linear approximation to f(2.18,8.29)≈4.2525Explanation:Solution:-