Determine whether the series k=1 3\k-1 converges and if so, find its sum.

Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

Q: Find the dimensions of a rectangle with area 1,728 m² whose perimeter is as small as possib m…

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Q: Inys 5. lim y→⁰⁰ y

A: To solve for the limits of the following function using L'hospital's rule.limy→∞ ln y5y

Q: 1. A farmer wants to fence in a field and divide it into four side by side, equal areas. If he wants…

A: From the given data And, xy=8000&f(x,y)=2x+5y is the parimeter to minimize.

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F =…

A: Here, the given vector field is: F=x2i+5xj+z2k⇒curl F=ijk∂∂x∂∂y∂∂zx25xz2…

Q: A. Find the slope of the line tangent to the given curve at the indicated point. 1. f(x) = 3x + 10…

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Q: Q3) Assume A = [4 6 3 11 7 2 [32] and B = 1 14 5 show that (AB)' = B' A' 31

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Q: For a particular financial methodology, the risk-reward function was defined as y=x(Inx-2), where y…

A: The risk-reward function,    y=xlnx-2y=units of reward, x=units of risk

Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

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Q: 12. Find the equation of the tangent line to the polar curve r = 2-sin(0) at 0 = 1/3. Draw.

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: the Following differential equation ²²=1+ P²

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Q: 1. Evaluate L²S³ (2y³ + x²y) dx dy

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Q: dy 1. If (x + y)² = x² + y² prove that 11 I Alx y

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: For the following function, find the equation of the tangent line at the point (1, 2). f(x)=√92¹-1…

A: Topic = Derivative

Q: x'dx √√x(1-x)

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Q: Evaluate the double integral: So Son VV (Hint: Change the order of integration to dy dx.) sin(7³) dr…

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

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Q: 3. SET-UP the definite integral that will give the area of the region specified using (a) z as the…

A: topic- area bounded by curves

Q: Given v (2, -9) and w = (7,-8), what is 2w - vv

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Q: 6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed…

A: Given:     Area = 4000 sq meter

Q: find the general solution of the given equation. y''+2y'+6y=0

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Q: Given Cost and Price (demand) functions C(q) = 100q+40000 and p(q) = -2.8q +800, what profit can be…

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Given: Now,     v(t)=f'(t)      =-16t2+286t+10'       =-32t+286

Q: Set up the integrals (No need to compute) for the volumes of solids of revolution by revolving the…

A: Given

Q: A real estate firm estimates that the value of a certain property will be given by the function 517…

A: To solve the following problem

Q: The height of the ball when its velocity is 0 ft/sec. is feet.

A: First, we will find the velocity of the ball at t second. Then we will find the value of t for which…

Q: Find derivative of each; A) m(t)= In(4t^3+tan(5t)) B) h(x)= 4sin^8(5x+1)

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Q: Let a(t)=20e^-0.3t ( in milligrams) be the amount of drug in a patients body at time t where t is…

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Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

Q: What is the exact value of sin(67.5°)cos(22.5°)?

A: Solution-

Q: 2. Use the graphs of y=f(x) and y= g(x) to sketch the graph of y=h(x). Hint: Estimate the function…

A: answer is in next step.

Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: To find the dimensions that minimize the amount of metal needed to make the can.

Q: A real estate firm estimates that the value of a certain property will be given by the function V…

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Q: Given f(x) = x^5 * cos x, dx= 0.01, use numerical differentiation to find: (1) df/dx for this…

A: Concept: The formula for the differentiation of the product of two function Let the two functions be…

Q: Question 10 The function y= ax6x³ has a minimum point at (2a, f(2a)). Determine the value of a. - a…

A: Let's find a value.

Q: Find the area of the region bounded by the parabola y² = 2x - 2 and the line y = x - 5. 16 17 18 19…

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Q: Find the center and the radius of the circle with the equation x2+12x+y2+6y−99=0   Enter the…

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Q: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…

A: Given problem:- ∫√x(x-5) dx

Q: Find the area of the region bounded by the parabola y² = 2x − 2 and the line y = x − 5. 16 17 18 19…

A: y² = 2x -2  y = x -5  Here we have to find intersection point  x = (y² +2)/2  x = y+5  Compare both…

Q: (a) Solve the first order linear ordinary differential equation x sin x + (sin x + x cos x) y = xe…

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

Q: The price of a popular gaming console is related to the quantity demanded by the equation 2p² + x² =…

A: We need to differentiate the equation and calculate the unknown.

Q: 3. Find f'(x) if f(x)= 3 2x + sin r

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Q: Sort St Question 2. Evaluate the following integral region). Show all your work! cos(x²) dx dy. Make…

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Q: (d) Use the given information to write an Lauation that relates the variables x and y.

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Q: Derive implicitly—Implicit differentiation. Please show a detailed solution. Also, comprehensive and…

A: In this question, we want to differentiate the given expression implicitly.

Q: y''-5y=sinx

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Q: A study indicates that the population of a certain town will be growing at the rate of p' (t) = 5 +…

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Q: * Let R be the region in the first quadrant bounded by x^2 +y^2 = 4, y^2 = -x+4 and y=0. Set up the…

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Q: cos sin-cos -d0

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Q: 100 (e) Σ199 2i(i3 – 1) i=1

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