If the length of the smaller edge, x is increasing with time, x = t² (where t = time in seconds). What is the change in surface area with respect to time?

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Q: Let f(x) = f'(x) = and - f"(x) = | 7x² 4-52 . Then 7x (5x-8) (-5r+4)2

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Q: ·/₁ Evaluate cos x sin³ x dx. 2 cos(x) + cos¹ (x) ²/ X syntax error. + C

A: Given query is to find the integral.

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A: First we meed to draw the inequalities on the graph÷ Red line÷3x+5y≥20 Blue line÷-2x+y≤2 Green…

Q: x y Suppose w==+ -, where y x = e¹, y = 2 + sin(3t), and z = 2 + cos(4t). Z A) Use the chain rule to…

A: given  w=xy+yzx=et  ,  y=2+sin(3t)  , z=2+cos(4t)by using chain rule…

Q: 44. S 1 (x²+4)3/2 dx

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Q: Question 7 Find the solution to (ylnx) (lny) dx + dy=0. Ox(lnx-1) + In|lny |= C ○ xlnx-x= - In|lny…

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Q: Suppose a company has fixed costs of $300 and variable cost per unit of x +1460 dollars, where x is…

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Q: r the graph of y = f(x) shown below in blue. Estimate the value of the derivative at x = 1. Then…

A: Given query is to find indicated derivative.

Q: Evaluate the integral using substitution and then Integration by Parts: Leve = x ² ) dx (Hint: Let u…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

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Q: ^= [] B =[27³ ²¹3). C= _¹5]. 6 12 8 2 a. Matrix A: Determinant (or why it can't be found): why not):…

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A: This is question of calculus  here one function is given  we solve using application of…

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A: Here we have to find the derivative of the function.

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Q: #4 find Y=3X₁ Y=3√x Volyne rotate about Y=3

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Q: Find the derivative of y with respect to 6 y = 4x³ sin-1 (4x³) + √√1 − 16x² dy dx =

A: To find the derivative of the given function.

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Q: The line tangent to the curve x²y² = 16 at (-1,-4) is y=.

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Q: Consider the function f(x) = a. Find f1(x). b. Graph f and f x +9 2-7x together. df 1 c. Evaluate at…

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Q: if x^2 + y^2 + z^2 = 9,  dx/dt = 5, dy/dt = 4, find dz/dt when (x,y,z) = (2,2,1)

A: If x2+y2+z2=9, dxdt=5, dydt=4. To find dzdt when x, y, z=2, 2, 1.

Q: Evaluate the integral: · [2²³√₁+1 1+16x²dr + C

A: To find the value of given integral.

Q: Use the table to evaluate the expression. X f(x) g(x) 1 2 3 2 3 1 3 5 5 4 1 6 5 6 2 1.0 6 3 4

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Q: The directional derivative of z = f(x, y) at (1,5) in the direction toward the point (7, 4) is 17…

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Q: -52 The region R in the first quadrant is bounded by the coordinate axes, the curve y = e x = 1. The…

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Q: s dx = S-₁₂ ² =S= X 2 – ν -1-3v+v² dv

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Q: rectangular fence is to be constructed with one of its face adjacent to an existing wall. Given that…

A: Given query is to find the dimensions for maximum area.

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A: Concept: By substituting bwith tand using an other variable besides t, such as u, we can convert the…

Q: Find the solution to (ylnx) (lny) dx + dy=0. Ox(lnx-1) + In|lny |= C O xlnx-x= - In|lny | + C…

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Q: it says it could be multiple choice is that the only answer?

A: see below the answer and explanation

Q: Find the Taylor polynomial T₂(x) for the function f(x) = 2e²x at x = 0. (Use symbolic notation and…

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Q: Use the Squeeze Theorem to evaluate the limit: Student solution. which is true for all x values…

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Q: Find the plane through the points (3,5,-2), (1,1,-4), (-5,-1,5)

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Q: Calculate the arc length of y = 16 - 6x over the interval [1, 3]. (Use symbolic notation and…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: The derivatives of the function f(x) = cos(3x²) that follow are incorrect. What misconception occurs…

A: Question number 6th  is not properly visible so we will be answering only 8th question.

Q: Find the solution to (2x + 3) y'=y+ (2x+3) ²; x = -1;y=0 2y = (2x + 3) 2 In (2x + 3) y= In(2x + 3) 3…

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Q: 3. (x + y - 6)dx + (x − y + 4)dy = 0.

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Q: The electrical charge at the point (x, y) is given by C(x, y) = 4x² + 5y² - 8xy. If an object moves…

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Q: If z = sin(x/y) and x=ln(u) and y=v^3 , find the following partial derivatives using the chain…

A: z=sin(xy)x=lnuy=v3∂ ∂x(sinx)=cosx∂ ∂x(xn)=nxn-1

Q: 5. Given the complex number A = 4 + j5, B = 2 - j3, and C = -2- j4. Calculate A + B and A+C. Show…

A: Please see the below picture for detailed solution.