8) A rectangle has a perimeter of 8 inches. What should be the dimensions so that its area is a maximum.

Q: 3. In evaluating the integral S x² dx (x-1)²(x²+1) you will decompose x² dx (x-1)²(x²+1) into…

A: No Partial fraction formula is incorrect. Actually it is, x2x-12x2+1=Ax-1+Bx-12+Cx+Dx2+1Multiply…

Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

Q: Consider the following matrix. -2 -3 A = 5 7 Choose the correct description of A. Find A if it…

A: First check that given matrix is singular or not then find its inverse.

Q: Estimate the integral right-hand sum with n = 3 subdivisions. Left-hand sum Right-hand sum - [₁2 2…

A: To solve the following problem

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: We have to find the value

Q: In(a³6³) (c) In(be)² a (d) (In c³) (In 62 -4

A:

Q: 5. Does the function f(x) = If yes, what are they? If no, explain your reasoning. have absolute…

A:

Q: lim (i-8j+² k) 4 lim (r 1-8j+² k) = 1+ 16

A: We have to find the limit

Q: s x3 √1-x² V dx

A: Given: I=∫x31-x2dx   ...1   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: The outer diameter of a spherical tank measures 6 feet. If the tank is made with a material % inches…

A: Given problem:- The outer diameter of a spherical tank measures 6 feet. If the tank is made with a…

Q: 1. x²y + 2xy - 5y³ = 0

A: As per bartleby guidelines we only give first question answers.

Q: 1) Find the average value of the function f define by f(x)=√√√49-x²³² On the interval [0, 7] 2) Find…

A: We can use the equation to find average value of a function in an interval.

Q: Verify Green's Theorem by evaluating both integrals √ y² dx + x² dy = √ √ ( Ox (ON-OM) c for the…

A: Here we have to verify the Green's theorem.

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A:

Q: d³y d²y dy+y=0 dx3 dx² dx

A: d3ydx3-d2ydx2-dydx+y=0                (1)LetD=ddxTherefore   equation (1)…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: To find the domain of rt and the value of rt0.rt=cosπt i-lnt j+t-16; t0=17

Q: Verify Green's Theorem by evaluating both integrals for the given path. [x² αx + x² or = // (+1) ++)…

A:

Q: The function f(x) = − 6x³ – 29.07x² + 433.242x – 5. is increasing on the open interval ( It is…

A:

Q: f(x)=e*; at (0,1)

A:

Q: Given the functions: Find: f(x) = 3x - 5 a. f(g(x)) g(x) = x² + 2x - 1 b. (f(h(x)) c. f(g(-1)) h(x)…

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Q: Find T(t) and N(t) at the given point. r(t) = (t² − 3)i+tj; t=3 T(3): N(3) = =

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Q: Using n = 2 equal-width subintervals, approximate the area of the region bounded by the graph of,…

A: This is a problem related to reimann sum calculation. Based on the general formula and concepts we…

Q: 3/3 10. Evaluate • 73 (x² +9)3/2 dx

A:

Q: S 7 tan (2x) dx 2 Hint: tan²x = sec ² x - 1

A:

Q: Use Green's Theorem to evaluate the line integral a-x)dx + (2x - x) d for the given path. C:…

A:

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

A:

Q: 3. In evaluating the integral S fractions. Let x² dx (x-1)²(x²+1)' you will decompose x² dx…

A:

Q: 27. Show that the tangent at any point 0 on the curve x = csec 0, y = c tan is y sin 0=x-c cos 0.

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Q: 1. Find the area of the region enclosed by the given curves. a) y - x² = 2x and x + 4 = y

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Q: a. Find the other functions of the triangle ABC, given that: 1. Sec A = 2 2. Cot A = 5/2

A: Solution is done in step 2

Q: 2. Evaluate fff 12ydV where the limits of integration is the region below 6x + 4y + 3z = 12 in the…

A:

Q: Find the equation of the tangent line to the graph of f(x) = x³e-* at a = 0.

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Q: Find the general solution to the differential equation. xy x-6 Preview TIP Enter your answer as an…

A:

Q: Find the area of the region that is enclosed by the cardiod r = 10 - 10 sin 0. NOTE: Enter the exact…

A: Given:       r=10+10sinθ  Area of cardiod A=∫∫Dr dr dθ…

Q: 3. f(x) = 3+ |2x − 4|, a = 2;

A:

Q: List the first four terms of the SEQUENCE {3n+1}n=1* Find the limit of the sequence or determine…

A: The given sequence is 2n/(3n+1)

Q: 4. Evaluate lim (cos x)¹/x². x-0

A:

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A: Given that the daily profit (in dollars) from the production and sales of x units of a product is…

Q: 3. In evaluating the integral ſ x²dx (x-1)²(x²+1)' you will decompose x²dx (x-1)²(x²+1) into simpler…

A:

Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant…

A: We can expand the log in the following steps

Q: Find the critical number of the function defined by f(x) = x² + 4x O-1 and 0 are the critical…

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Q: Solve the differential equation in Higher order differential equations (D^2-D-2)y= cosx PLEASE…

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Q: ² fx ds, where C is с t a. the straight line segment x = t. y = from (0,0) to (16,4) b. the…

A:

Q: Show complete solution. Let S be the surface with equation y = (4x2/9) + z2 a. Write the equation…

A:

Q: S sin (3x) 1+cos² (3x) dx

A: The detailed solution is given below Thank you

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. If it…

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Q: Prove the following statement: 2² +23+24+... 2+1 = 2" +2-4

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given

Q: 4. The Bernoulli's form of the differential equation x²dy + (2xy-y³)dx=0 is

A: