1) Calculate the following integrals. b) √₁6x²=1 -dx

Q: What two nonnegative real numbers with a sum of 66 have the largest possible product? The numbers…

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Q: suppose f(x)= x^3+ax+b where a<0 and has stationary points at (-2,3) find a and b and find position…

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Q: A 42 cm piece of string whose length is given below is cut into two pieces. One piece is used to…

A: Here we have, A 42 cm piece of string whose length is given below is cut into two pieces. One piece…

Q: A 54 cm piece of string whose length is given below is cut into two pieces. One piece is used to…

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Q: Problem 3. Solve [2*+2³ = 10 4* +4" = 68

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Q: To find the distance across a small lake, a surveyor has taken the measurements shown in the figure…

A: As per given question  We have to solve above question and find distance across the lake

Q: Consider the polar curves C₂: r = 4 cos 0 and C3 : r = 4 sin 0. (a) Set up the integral that gives…

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Q: B. The maximum value of f(x) is h. OC. The graph of y = f(x) is a parabola. D. If a 0, then f has a…

A: Topic:- calculus

Q: dy = -3, dt If z² = x³ + y², dx dt Please give an exact answer. Provide your answer below: dz = 2,…

A: We can solve as follows

Q: 2 Evaluate thefallowing cartesian integrats by - changing theminteequivalent Palar integralse 4- to…

A: Solving

Q: For items 1-5 A 10-ft ladder is leaning against a house on flat ground. The house is to the left of…

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Q: Determine the indefinite integral 4 √√x + 3 6x 1/0² - 1717 dx 4 X

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. a. So f(x) dx…

A: Let's find.

Q: Question 6.5: In Example 6.4 we did an ideal thermodynamic analysis of the General Electric T700…

A: answer is in next step

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: The equation of motion of a particle is s = t³ - 27t, where s is measured in meters and t is in…

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Q: Solve the triangle with the given information. a= 8.3, c= 2.8, p= 19.4° b 5.7 (Type an integer or a…

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Q: g expressions a. lim (2z - 1)(2-1)

A: Given : apply chain rule    find limit of about separately

Q: Use the formula к(t): k(t) ||r' (t) x r"(t)|| 3 ||r' (t)||³ r(t) = esti + e¯tj = to find (t). #1

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Q: A company selling baseball gloves has fixed costs of $1800, and it costs an additional $23.71 to…

A: This question is related to Cost and Revenue function, we will solve it using given information.

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: rite down the ma TIX represe the linear that projects every vector in R³ orthogonally onto the…

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Q: 109. f(x)=x* tan x³ -x In (1+x2), then the value of (b) 1 dª f(x) dx 4 at x = 0, is: (d) 15

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: In a circle of radius 25, find the length of the arc spanned by a central angle of radians. Round…

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Q: Find the area of the region bounded by the graphs of the equations. y = -x² + 6x, y = 0

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Q: Evaluate fff 12y - 8x dV wherein the limits of integration are the region behind y = 10-2z and in…

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Q: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

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Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = , y =…

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Q: Solve me initial No need to Jimphiry. by value the separaion of variables a.

A: To solve the following initial value problems by the separation of variables.a y'=1+y2, y0=1b…

Q: -3x+1) -3х 2-3* dx

A: According to our company policy we are supposed to answer only first question and rest can be…

Q: i-2yj + (z+3)k and suppose the outward flux of F through Side A is 1 and through Side B is -3. Can…

A: answer is in next step

Q: Let f(x) = 3x² - 9x + 11 The slope of the tangent line to the graph of f(x) at the point (2,5) is…

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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: Consider the vectors. (-6, 2), (8, 1) (a) Find the dot product of the two vectors. -46 (b) Find the…

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Q: At what points c does the conclusion of the Mean Value Theorem hold for f(x) = x³ on the interval…

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Q: Evaluate (1 + i)(¹ - i). (1

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e cos(t), y = et sin(t), z =…

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Q: -(;) > Let 7 (t) = < - 5ť² + 3, t² – 3t, In| a. Determine the coordinates of the point on the curve…

A: given: r(t)=-5t2+3,t2-3t,ln15

Q: For two exclusive events A and B, P(A) = 0.2 and P(A U B) = 0.65 If the given information is shown…

A: Solved below

Q: 42. If g(0) = 0 sin 0, find g"(π/6).

A: Solve the given

Q: Determine whether the series converges or diverges. 4n³ n²-4 n=2

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Q: Determine if the following series converges. If the series converges, determine if it converges…

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Q: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

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Q: Let the graph below represent f(x). For which values of x is f(x) increasing? 20 16- 12- -5-3-2 8+…

A: The graph of the function f'x is To evaluate: The values of x for which fx is increasing.

Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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Q: Find the area (in square units) of the region under the graph of the function f on the interval [3,…

A: Area under the curve over the given interval:3, 6Area: ∫abf(x) dxA =∫36 (8ex-x) dx   =8ex -x2236…

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: Let f (x, y, z) be a function such that : (i) the function f (x, y, z) decreases most rapidly at the…

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Q: Find the equation of the final function after all the following transformations have been made on y…

A: The below image has all the steps