A rectangular box with no top is to have a surface area of 49 m². Find the dimensions (in m) that maximize its volume. (width, length, height) = m

Q: Let F = (3yz)i + (7xz)j + (7xy)k. Compute the following: A. div F B. curl F 0 =0i+ C. div curl F j+…

A: As we know that, The expression for the divergence of the vector point function F→=F1i+F2j+F3k…

Q: The domain of In(x) + True False 1 x² - 1 consists of all real numbers except x = ±1.

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Q: Finding Area by the Fundamental Theorem Find the area of the region. y = 5e-x/4 -4 -2 y 10r 8 6 4 2…

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Q: Solve f8x cos(7x) dx using Integration by Parts.

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Q: The first derivative of a continuous function y = f(x) is given. Find y'' and then sketch the…

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Q: ∞ k=1 (-1)+¹(x - 1)k k

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Q: Which of the following equations has no solution? 5. a. b. − ²)(a b) = (19) (²2) -77²) (²5) = (69) a…

A: We know that value of determinant is zero when any two row (or column ) are identical. Here in case…

Q: f'(x) <0 for x# -5 Choose the correct graph below. A. Choose the correct graph below. A. -10 Choose…

A: Given query is to find the correct graph: Solving A and B since graph of C and D are not given .

Q: Find the work done by the vector field F = (4z, 4y, 3x) in moving an object along C in the positive…

A: Solve the following

Q: Find the slope of the tangent line to the curve 2xy - 3y³ = -9 - -4x² - at the point (2, -1).

A: NOTE: Refresh your page if you can't see any equations. . the given curve is  and the given point…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 — 4t, where 0 ≤ t ≤ 1.5…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x…

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Q: f(t) = 96t-21³, -5st<∞⁰0 a. Find each local maximum, if there are any. Select the correct choice…

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Q: Use one-sided limits to determine whether the following limit exists and its value. If the limit…

A: Given query is to find indicated limit.

Q: 0 Question 18 Find the following for the equation f (x) = -x² +9x - 8 Write infinity instead of…

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Q: 4. Using the alternative formula for curvature k(t) = = for the helix F(t) = (4 sin t, 4 cos t, 0).…

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Q: Find the differential df of the function f given the gradient. Vf= (2x + 2e") i + 2xej.

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Q: For the function f(x)=x−2/x, find all values of c in the interval [2,4] that satisfy the conclusion…

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Q: 19 60

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Q: Determine the values of constants a, b, c, and d so that f(x) = ax³ + bx² + cx+d has a local maximum…

A: GIven f( x ) = ax3 + bx2 + cx + d GIven function has a local maximum at the point ( 0 , 0 ) and a…

Q: Locate all the critical points of the function f(x, y) = 6x - x² 3xy². (If there are several points,…

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Q: Given ƒ(x) = √² t² - 49 1 + cos² (t) At what value of x does the local max of f(x) occur? x = dt

A: We have to find the local max of f(x).

Q: Let A-R\(-2), and define f: A-R by the formula f(a) a but not onto. 2a a+2 Prove that is one-to-one

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Q: The gas law for an ideal gas at absolute temperature 7 (in kelvins), pressure P (in atmospheres),…

A: NOTE: Refresh your page if you can't see any equations. . P=pressure T=temeprature V=volume R, n=…

Q: Find f(x) such that f'(x) = 9x² O f(x) = 3x³ - 2x² + 4 O f(x) = 3x³ - 2x² + 10 O f(x) = 3x³ - 2x² +8…

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Q: Consider the following parametric curve. Use the information to answer parts ​(a) and ​(b).…

A: Consider the following parametric curve. By using the information to answer parts (a) and b.x=cost,…

Q: Use integration by parts to evaluate the definite integral S te-t dt.

A: We need to use the integration by parts to solve the definite integral.

Q: Setup the Riemann sum 5 n [²³x³ dx = lim Σ n→∞ k=1 b f(x) dx n = lim Σ f(x)Ax for the given…

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Q: a. Identify the function's local extreme values in the given domain, and say where they occur. b.…

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Q: a 60° b Find a and b. с 30° Note: Triangle may not be drawn to scale. Suppose c = 3

A: using sin law in triangle sinAa=sinBb=sinCcgiven A=30°            B=60°            C=90°…

Q: What is the sum of the series -4? THE NIG 20 13

A: Topic = Series

Q: (a) Compute 83 of ∞ (c) Use n = 3 and n=1 2 9n6 (b) Estimate the error in using $3 as an…

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Q: Find the determinant of the matrix, if it exists. (If an answer does not exist, enter DNE.) 1 N -1…

A: If the given matrix A=abcd then the determinant of the matrix will be: A=a·d-b·c   Let, A=871-1-78

Q: Let P(t) represent the price of a share of stock of a corporation at time t. What does each of the…

A: Solution: Given data, Let P(t) represent the price of a share of stock of a corporation at time t.

Q: 2. Fully factorise 4x4 − 8x³ - 7x² + 11x + 6.

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Q: dx x(In x²)8

A: NOTE: Refresh your page if you can't see any equations. . ................(1)

Q: Find 3u, -5v, u + v, and 5u - 4v for the given vectors u and v. (Simplify your a u = i + j, v=i- j…

A: given vectors        u = i + j  and   v = i - j   then finding -   (1)  3u = 3 (i + j) = 3i +3j…

Q: ots. S=C₁e-t + c₂e²t + c3e6t+₁е-5t O a. 2,-1,6, -5 O b. -2,-1,-5,6 O c. 5,-1, 2, 6 O d. 2,-1,2,6

A: Topic:- application of differential equations

Q: The midpoint of AB is at (-4,-2). If A = (4, 6), find B. B is:(

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Q: Find the length of the loop of the given curve. x = 9t-3t³ y = 9t² 6 5 e +39 X

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Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

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Q: Let f(x) = = f'(x) = - 2 log(x) ƒ' (5) Round to 4 decimal places if needed. =

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Q: Find the radius and the center of the circle given by 2x² +8x+2y² −12y+25=0

A: Given query is to find the radius and the centre of the circle.

Q: Use the chain rule to find First the pieces: dw dr მu მყ θω Əz dz dt dy dt dz dt Now all together:…

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Q: Use the Fundamental Theorem of Calculus to find •16 sin(x) S." dx =

A: Topic - Definite integral we are given, ∫116sinx4x34dxFormulas usedddxxn=nxn-1∫sin(x)dx=-cos(x)+C

Q: The minute hand on a watch is 8 mm long and the hour hand is 4 mm long. How fast is the distance…

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Q: a. Write the series using sigma notation: 1 1 1 1 3 27 81 1 + 1 9 + -= n=0 b. The sum of a series is…

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Q: Setup the Riemann sum n ['so k=1 f(x) dx : = •5 x³ dx = lim ((2+3/nk)^3)*(3/n) n→∞ n lim f(x)Ax for…

A: Riemann sum of ∫abf(x)=limn-&gt;∞∑k=1nf(xi)∆x, where ∆x=(b-a)/n

Q: Suppose F(t) has the derivative f(t) shown below, and F(0) = 2. Find values for F(2) and F(7) -1 3 2…

A: Given F(0) = 2 as we know that F(b) - F(a) = ∫abf(t)dt

Q: Find given that y=[atan-¹(bx)]². dy dx Assume a,b ER. 2[atan-¹(bx)] O 2[atan-¹(bx)]- O 2b[asec²(bx)]…

A: To find dydx given that y=a tan-1bx2.Assume a, b∈ℝ