If 3x O -2. O 0. O 4. O 2. O -4. 3 [2x y/t then y =

Q: Solve for the general solution of the given DE: O x In y + In In yl = y + c Ox In x + In In y = x +…

A: We can find the solution of the given differential equation by using the variable separable method.

Q: nd the arc length along a circle of radius 14 units subtended by an angle of 160°. Round your answer…

A: Given query is to find the arc length.

Q: Kaiden wants to enclose a rectangular field with two internal partitions as shown. If there is 17300…

A: We have given the fencing length i.e., 17,300 feet and area is maximum then find the length and…

Q: Find the area of the surface obtained by rotating the curve from x = 0 to x = 9 about the x-axis.…

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Q: Let f(x) = 9x² + x³ +20 + 24x Determine the absolute extrema of f on [-5, -1]. If multiple such…

A: The given function fx=9x2+x3+20+24x We have to find the absolute maximum and absolute minimum values…

Q: 3. Evaluate the following integral sin x cos x - sin x + cos x O a. -In|sinx + cosx| + C O b.…

A: To evaluate the given integral.

Q: Q2. By finding an apporppriate integrating factor, solve (3x²y + 2xy + y³) dx + (x² + y²)dy = 0.

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Q: Find the area of the region bounded by the curves y = x² - 6x + 6 and y = -x² + 4x - 2.

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = y cos(x - y),…

A: Given z=y cos(x-y)      ; (4,4,4)

Q: Let w(x, y, z) = x² + y² + z² where x = sin(2t), y = cos( - 7t), z = e-8t. dw dt dx dy dz & dt dt dt…

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Q: b.) If r(x)= 1 √g(2x) > find r'(x) at x = 2

A: Topic = Derivative

Q: Σ 1 8

A: See this solution in below.

Q: interval. f(x) = x³ - 6x² + 9x + 22, on [-1,2] 3. Find the absolute extreme values of the function…

A: Given: fx=x3-6x2+9x+22, on -1,2   Use the Power law: ddxxn=nxn-1 For maximum and minimum values…

Q: Fill in the spots in the integration process below based on the indefinite integral 4x²-25 S using…

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Q: Consider the function f(x) = needed. x² x² + 4 You may use the facts that f'(x) = a. Find the…

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Q: Find the scalar and vector projections of b onto a. a=(3, 6, 2), b=(3, 1, 1) compab= proj b=|

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Q: equation, find dy/dx evaluated at the given values. y²-x5= = -7 at x = 2, y = 5

A: Topic:- application of derivatives

Q: a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard…

A: a) Given:     The dimension of the cardboard is given as:      Length=41 ft      Width=22 ft Assume…

Q: Is there a number a such that the following limit exists? (If an answer does not exist, enter DNE.)…

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Q: 15 √x +9 Find the average density Pave (in kg/m) of the rod. kg/m The linear density p in a rod 7 m…

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Q: Find dy dx dx by implicit differentiation. ex cos(y) = x + y

A: We have to find derivative by implicit differentiation.

Q: 2 10x The function f(x) = x²e¹⁰x is increasing on the interval and is decreasing on the interval The…

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Q: 7. Compute fa, fy, and fz. (a) (x² + y² +22)-1/2 Straight forward (b) sin-¹(xyz) Straight forward…

A: Please see the below picture for detailed solution.

Q: Suppose the derivative of the function y=f(x) is y'=(x-4)²(x-2). At what points, if any, does the…

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Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: Activity 1: Pictures Analysis (eliciting prior knowledge, Motivation, Hook) Observe the pictures…

A: 1. The given diagrams show the following applications of the functions: Continuity of functions,…

Q: The parametric equations of lines L₁ and L₂ are as follows: L₁ x= 1+ 4t y=2+7t z = ½-5t and L₂: x= 7…

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Q: Find the indefinite below using the substitution x = tan (8). x √ √1² dx, for −1<x<1.

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Q: 10 & 16 (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum…

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Q: Find dy by implicit differentiation. x² x+y dx 11 = y² + 5

A: Given query is to find the derivative.

Q: Use sigma notation to write the Maclaurin series for the function COS IIX.

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Q: For a small farm, the cost in dollars to produce x containers of ice cream is C(x) = 0.6x +14. The…

A: I am attaching image so that you understand each and every step.

Q: Use the chain rule to find the derivative of 6√10x8 + 8x7 Type your answer without fractional or…

A: Topic- Derivative of a function We are given f(x)=610x8+8x7Formulas used:chain rule:…

Q: 4. Find an equation of tangent line at the point (-1, 1) to the curve x¹y² + 1 = x² + y³. 5. The…

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Q: 1 The graph of y = 2x²(x + 1) and y= X (x > 0) intersect at one point, x = r, as shown to the right.…

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Q: Sketch the graph of the function below, including correct signs, x-intercepts and y- intercepts.…

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Q: Use l'Hôpital's rule to find the following limit. lim (In 6x- In (x+4)) X→∞ lim (In 6x-In (x+4)) =…

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Q: 2) f(x) = sin−¹(x + 1) + ½/ Table: y = sin ¹x Transformations: D: R: X

A: y= Sin-1x

Q: find the accumulated amount after 3 years on an investment of 5000 earnings an interest rate of 5%…

A: given query is to find accumulated amount.

Q: Graphs of f(x) = 5x and g(x) = 5√ intersect at the points (0,0) and (1,5). The region between those…

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Q: O x = 4 ve Find all points where the function is discontinuous. e

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Q: Let g(x) 10x + 12 3x + 6 Find the derivative of g'(x). g'(x) =

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Q: 4 2 -5 -4 -3 -2 -1 -2 -4 -6 -8 -10+ 1 2 e function graphed above is: cave up on the interval(s) cave…

A: The function is concave up where -2&lt;x&lt;1.   The function is concave down where 1&lt;x&lt;5.

Q: What is f'(x) if f(x) = -? 40x5 ex

A: Given data, fx=40x5ex

Q: Solve the corresponding differential equation given the general solution via elimination of…

A: The objective of the question is determine the differential equation.

Q: Find the surface area of the part of the plane 5x + 3y + z = 2 that lies inside the cylinder x² + y²…

A: Plane: 5x+3y+z=2 Cylinder: x2+y2=4

Q: Car A travels at an average speed of 65 miles per hour. Car B travels at an average speed of 55…

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Q: Write a function in any form that would match the graph shown below. -10 -8 -6 Answer: f(x) = -4 -2…

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Q: If f(x) = (3x + 5)¯², find ƒ'(x). Find ƒʼ(2).

A: As we know that: The Chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1   The given function is:…

Q: 3. Evaluate the determinant. 24 | a. 22 b.-12 c. -2 d.-18. e. -4

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…