Let f be the function given by f(x)=sin(2x)cos(1+x). What is the average value of fon the closed interval 1≤x≤3 ?

Q: For the following exercises, the vectors u and v are given. a. Find the vector projection w= proju v…

A: Given: u=5i+2jv=2i+3j

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

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Q: Find and classify the critical points of z= (a²-8x) (y² – 4y) Local maximums: Local minimums: Saddle…

A: The given function is;  z=(x2-8x) (y2-4y).

Q: Use calculus to find the area A of the triangle with the given vertices. (0, 0), (5, 3), (1,8)

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Q: Without actually solving the given differential equation, find the maximum radius of convergence R…

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Q: A movie theater has a seating capacity of 335. The theater charges $5.00 for children, $7.00 for…

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. y² + 8y +49 (y² +49)²…

A: The given integral is:∫y2+8y+49y2+492 dy

Q: Let f be the function with domain [1, 3], defined by f(x) = −x² + 3x. The function f has a global…

A: The answer is in step 2.

Q: 3√t-1 S (³√t=¹) dt

A: The given integral is:  ∫3t-1t dt

Q: Each of the limits below represent a piece of the passcode that you must enter to proceed. The…

A: We have to find the limits to get the passcode.

Q: 4. Find the exact arc length of the curve over the stated interval: x=3t², y=t³,0 ≤t≤2

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Q: Using the ratio test to determine the convergence or divergence of the series series. Divergent The…

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Q: 6 Function f is defined by [1-e, x0

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Q: An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the…

A: We have given that height of the ball after t seconds is s=-2.7t2+30t+6.5

Q: (a) Find the arc length function for the curve y = In(sin(x)), 0 < x < πr, with starting point (,0).

A: Given equation of curve:- y=lnsinx

Q: Find an equation of the tangent line to the graph of the given function at the specified point. x²-1…

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Q: Evaluate the iterated integral **²y³ dady.

A: K=∫04∫016x2y3dxdywe know ∫xndx=xn+1n+1+c

Q: y-329 and recieved an incorrect mark. Also remember we are solving for Z so put the answer as an…

A: Given:z=7ex2-2y

Q: Find the surface area for the portion of the surface z − 2x + y2 = 21 that lies above the triangle…

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Q: A ball is thrown into the air and its position is given by h(t) = −4.5t² + 87t + 19 where h is the…

A: Application of Derivative

Q: For what values of p does the following series n=2 (Inn)p-2 n converge or diverge?

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Q: Let f(x) = x² - 5x - 6. Find the open intervals on which f is concave up (down). Then determine the…

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Q: Differentiate the function. f'(x) = f(x) = e5

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Q: Find an equation for the graph sketched below: -5-4-3-2 ME 6 S -2 -3 -4. 5 -6 -7 -8+ N a

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Q: - Find formulas for dy and Ay if y = x² − 7x + 4. **** dy Ay

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Q: Solve the differential equation y` = (196+ y)²

A: The given differential equation is: y'=196+y2

Q: A stone is thrown straight up from the roof of a 256-ft building. The distance (in feet) of the…

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Q: . Find the polar equations x-3y+2=0

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Q: Consider the following. Sk (4x - y) da, where R is the region in the first quadrant enclosed by the…

A: Given that  R is the region in the first quadrant enclosed by the circle x2+y2=4and the lines x=0…

Q: Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist,…

A: We find the first and second derivatives using the power rule F(t)=3t5-20t3+20F'(t)=ddt3t5-20t3+20…

Q: Use linear approximation, i.e. the tangent line, to approximate 4.7² as follows: Let f(x) = x². The…

A: f(x)=x2m=f'(x)d dx(xn)=nxn-1

Q: 8. Solve the following. (a) Find the equation of the tangent line to the graph of f(x) = x²-9 at x =…

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Q: 3. Evaluate the limit, if it exists: lim a. 0 b. 7 x² + x + 1 x+2 X²-2 c. 3.5 d. does not ex

A: H=limx→2x2+x+1x2-2

Q: Solve the differential equation. 2xy + 4x + (x² − 4) d (x² - 4) dy = 0 dx Mangle METALT TANG

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Q: Find all the complex roots. Write the answer in exponential form. The complex cube roots of 16+16i

A: Given:  z = 16 + 16i

Q: Consider the following. f(x, y) = 9x y A /2 sin(0) 1/2 ([ 0 r = sin 0 (a) Set up an iterated…

A: Given f(x,y)=9x

Q: 4. Find the exact and the approximate value of x: 2* = 5*-1. Round answer to three decimal places. N

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Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (4,…

A: To Find : Distance of point (4,6,3) from the plane x-y+2z=10

Q: 1. Find the length of the arc of the curve 3 (2 x − 1)² from x = 0 to x = 8 - y = 32/2 (2x

A: Given :y=2322x-132

Q: Let f(u) = √u and g(x) = u = 4 + 9x². Find (f o g)'(3). (fog)'(3) = (Type an exact answer.)

A: f(u)=u3g(x)=4+9x2(f∘g)(x)=f(g(x))

Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: Given:  fx=2-62x To Find:  To determine the domain of the derivative of fx and  then to evaluate it…

Q: Find the sum of the convergent series. (Round your answer to four decimal place Σ (sin(7))" n = 1

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Q: An object traveling in a straight line travels s(t) kilometers after t hours, where s(t) = 8t² + 5t.…

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Q: Integral e^x/9+e^2x=

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Q: Let à = (-3, -5, -2) and 6 = (2, 5, 3). Find à x b. V Calculator Check Answer 7

A: Please see the below picture for detailed solution.

Q: Find the limit. lim X→0 sin (8x) 7x

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Q: 3. If z=x²y,x=2t+s, and y=1-st², find dz atl=2

A: As per our guidelines, we are supposed to answer only one question at a time. Since you have posted…

Q: Find the tangent plane to the equation z = 7e²²-2y at the point (4, 8, 7) 2 II

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Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

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Q: Find y if In X Jer X (2x + 7) dx +4% + +4x + 8 8 | + ² tan y + c

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