The following integral may be solved using substitution. Choose a function u that may be used to solve the problem. Then find du. 3 ... Let u =, so that du = dx.

Q: Find and classify the critical points of the function: f(z, y) = z' + y* – 144ry + 4 Local maximums:…

A: Given that; f(x,y) = x^4 + y^4 - 144xy + 4  Let's  find minimum and maximum points;

Q: Using the separation of variable method solve the differential equation d?/d?=4x3y3

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Q: Evaluate the integral: So V1+ 8xdx 3 *Input answer as a decimal. Round-off to 2 decimal places.

A: Given query is to find the value of the integral.

Q: x dy + ५ ax X cost d x dy 6- -2 ५

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Q: 2 v2x-x2 XY xydydx 0 0

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Q: Find the limit. Answer in either fraction or integer form. NO DECIMAL APPROXIMATIONS. f the limit…

A: Given query is to find the limit nof the expression.

Q: 16x²+9y²=144, (first quadrant area)

A: ∫a2-x2 dx = 12xa2-x2 +a22 sin-1xa+C

Q: 2+Secx-

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Q: Evaluate the given limit |. lim %3 1- x2 2. lim CosX

A: 1. limx→0+1x-1ex-12. limx→∞x1cosx

Q: Solve the given DE: dy e* – 2x cos y eу — хx2 sin y' dx ||

A: Differential equations is solved.

Q: Determine the maximum curvature for the graph of f(x) = 5 In (x). The maximum curvature is at x =

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Q: 1. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If…

A: Given:  Data is given

Q: The flow rate of water at a pumping station on a given day, is given by the function R(t) = -t? +…

A: This is a problem related to integration. Based on the concept and formula we will answer the…

Q: Find the simplified difference quotient. f(x) = 2x +6

A: answer is in next step

Q: Find the point at which the line meets the plane. x = - 3 + 5t, y = 3+ 6t, z = - 2 + 3t; x + y +z =…

A: Given ; Line meets plane = ?   x = -3 + 5t   y = 3 + 6t   z = -2 + 3t   Plane;        x + y + z =…

Q: C. Solve as indicated. 2. Find the first 10 terms of a sequence in which the fourth term is 114 and…

A: Let us consider an A.P series with first term= a and common difference=d  Then the nth term =…

Q: 3. Out of frustration, Maxine throws a stone into a river. This caused ripples in the form of…

A: Given problem:- 3. Out of frustration, Maxine throws a stone into a river. This caused ripples in…

Q: Complete the sigma notation for this series: 4 + 9 + 14 + . ...+ 294 + 299 n=1 A =

A: We have to find out A

Q: II. Find the area bounded by each of the following curves. Show your complete solution. Write your…

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Q: 3. A girl is flying a kite on a string. The kite is 120 ft. above the ground and the wind is blowing…

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Q: Find the velocity and acceleration vectors in terms of u, and ue. do a0 r= 9 e and :3 dt v=Ju, +Jue…

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Q: V29. Verify that the piecewise-defined function (-, x<0 y = 2, x 0 is a solution of the differential…

A: As per the company's guidelines, we are suppose to answer the first question. Kindly repost the…

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: (c) SUPPLY RATE When the price of a certain commodity is p dollars per unit, the manufacturer is…

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Q: y-1 3. Solve the initial value problem of=4 y(-1) = 0 dx

A: dy/dx = (y-1)/(x+3) dy/(y-1) = dx/(x+3) ln(y-1) = ln(x+3) + lnc here we find c using initial value x…

Q: Problem 12 Find the following indefinite integrals (a) S(9x² + 8x +3)dr (b) S(x-4 – 9/I)dr (c)…

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Q: lim (5x + 1)cot* x-0+

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Q: he velocity vector? Di+O i+O k

A: Topic:- application of derivatives

Q: Fill in the blanks: The derivative of a product of two functions is the first function times the of…

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Q: A window consists of a rectangle surmounted by a semicircle. If the perimeter of the window is 32…

A: We have to calculate radius and height

Q: Find the Taylor series of  f(x)=ln(2+x) around the point x=-1 by reaching the term n=4

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Q: Find the equation for the horizontal asymptote of the graph of the function. (If an answer does not…

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Q: du Identify u and dx - for the integral u du dx. dx u = du dx

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Q: cos vx cos(sinvx) dx

A: Given query is to find the value of the integral.

Q: 12 Consider the graph of the ellipse. which is drawn to scale. This ellipse has an eccentricity of…

A: Given query is to find the equation of the ellipse.

Q: Find the equation of the tangent line to the function f(x) = 4* at x = 3.

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Q: dy as a function of x. dx Write the following function in the form y = f(u) and u = g(x). Then find…

A: Given query is to find the derivative of the expression.

Q: The area of the region that lies to the right of the y-axis and to the left of the parabola æ = 2y –…

A: topic- Area bounded by curves

Q: 11. (e* sin y – 3x²)dx + ( e* cos y+ |dy = 0 12. (2x + 1+x?y? ) dx +( -29) dy = 4 - 29) dy = 0…

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Q: x/2 2. dy Sin x dy +34 2- X 2

A: A detailed solution is given below

Q: Write a in the form a = a-T+ anN at the given value of t without finding I and N. r(t) = ( - t+ 4)i…

A: Here, r(t)=(-t+4)i+(2t)j+(t2)k⇒r'(t)=(-1)i+(2)j+(2t)k⇒r''(t)=(0)i+(0)j+(2)kSo,r'(-1)=-1,2,-2 &amp;…

Q: Find the velocity and acceleration vectors in terms of u, and ug- = 5 sin t and 0= 5t = ( 5 cost)u,…

A: Topic:- application of derivatives

Q: Use the method of substitution to find the indefinite integral. Check your result by…

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Q: be the solid enclosed by the paraboloid z = -x² – y² and the cone 2? = x² +y?,z > 0.

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Q: Jse the functions below to (a) express as a function of t, both by using the Chain Rule and by…

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Q: kt Convert the equation f(t) = 310(1.13)' to the form f(t) =

A: answer is in next step

Q: Evaluate dx 2 1-x

A: We have to evaluate ∫23x1-xdx. We know that ∫dxx2-a2 = 12aln x-ax+a+C

Q: sin(4z) 7. lim I-0

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Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (9e' cos…

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Q: Evaluate the given imit 1. lim (x-1)? 2 メ→! In x 2. lim 3X - 2 × 3. lim (4x+1) ot x

A: As per guidelines, I can answer only one question. Since you have asked for multiple, So I did first…