Find the limit. sin(8) lim 0 0 90 + tan(0)

Q: 1. Use an appropriate substitution to solve these four ODES: (a) dy dx = x + 3y 3x + y

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Q: Evaluate the iterated integral In 3 In 5 Ţļ 3y dy dx

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Q: Find the volume of the region bounded above by the paraboloid z and below by the square R-4≤x≤4…

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Q: Consider the equation z*=x+y, where x,y and z are all functions of r. Which of the following is the…

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Q: Let f be a function with f(x) > 0 for all x. Let g = 1/f. (a) If f is increasing in an interval…

A: The given data is:  Let f be a function with f(x)>0 for all x. Let g=1f

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

A: As we know that, To expression to calculate the equation of the plane when it passes through the…

Q: art 1 or what value(s) of x does the graph of have a horizontal tangent? C = art 2 Differentiate the…

A: For calculating horizontal tangent for  f(x)=10x^3-15x^2-60x-30 Where it's derivative is equal to…

Q: O stretch horizontally by a factor of 9, then shift down 6 units O shrink horizontally by a factor…

A: We will find the required

Q: Use Lagrange Multipliers to find the maximum value of f(x, y, z) = 2x + 2y + z, subject to the…

A: NOTE: Refresh your page if you can't see any equations. . the given function is find the partial…

Q: Differentiate. Please use positive fractional exponents of lowest terms rather than decimals in your…

A: y=-8t+6t5+9t6d dt(tn)=ntn-1

Q: For the ellipse equation: 4x^2 + 9y^2 = 36 find the center, vertices, foci and graph it.

A: The given equation of ellipse is:4x2+9y2=36x29+y24=1

Q: Find an equation of the plane. The plane that passes through the point (-1, 2, 1) and contains the…

A: Please see the below picture for detailed solution.

Q: 0 8x dx x4 -8x² + 32 X

A: To evaluate the following integral. ∫028x dxx4-8x2+32

Q: for the following question above help me solve d and e

A: Given graph of f'(x)

Q: The total profit (in dollars) from the sale of x skateboards is P(x) = 30x – 0.3x² -250, for 0 ≤ x ≤…

A: Given Profit function:- Px=30x-0.3x2-250

Q: Find the general solution of the following differential equation. Primes denote derivatives with…

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Q: d²y Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: 2. Let a > 0 be a fixed real number. Determine whether dx xl+a [3 converges or diverges. If it…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the derivate a) F(x) = 5-8x 1+ 2X f'(x)= 6) write all x-values (if any) at which the tangent…

A: (a) f(x)=5-8x1+2xd dx(ab)=bdadx-adbdxb2d dx(xn)=nxn-1

Q: A ball is dropped from the top of a lighthouse that is 145 feet above sea level. The height…

A: Given height function s( t ) = -16t2 + 145

Q: Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify…

A: Given function:- fx=x2-4x-2

Q: Verify that the given differential equation is exact; then solve it. (21x²y³ + 4y) dx + (21x³y² + 4y…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as a…

Q: Use a graphing utility to graph the region bounded by the graphs of the equations. Then find the…

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Q: Consider the function f(0) = 7sin²0 - 7cos0. (a) Find f'(0) = 7 sin (20) + 7 sin (0) (b) Find the…

A: f(θ)=7sin2(θ)-7cosθ(i)  d dθ(sinθ)=cosθd dθ(cosθ)=-sinθ

Q: Let R be the region in the first quadrant bounded by the graph of y = e, the z-axis, the y-axis, and…

A: Given :- Region R in the first quardrant bounded by the graph y=e-x,the x axis , the line x=b

Q: Estimate the area under the graph of F(X)=X2 +6X+11  over the interval [0,8] using four…

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

Q: Determine the sum of the convergent series below. n=1 24n201-n

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Q: Find parametric equations of the line that satisfies the stated conditions. The line that is tangent…

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Q: For the following graph, identify the points where the local and absolute maxima and minima occur.…

A: From the given graph we can conclude as

Q: Part 1 Differentiate f(x) Answer: Part 2 df dx f'(x) = x³ - 4x + 5 x3 If f(x)=√x sinx, find f'(x).

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

Q: For the equation of the hyperbola: 4x^2 - y^2 = 16. Find the center, vertices, slope of asymptote’s,…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: To solve the following problem

Q: An explosion sends two shards of metal to the east and to the north. The northward shard travels at…

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Q: Evaluate the double integral over the given region R R (18y²-14x) DA R: 0≤x≤4, 0≤y≤2

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Q: You are given the graph of the derivative function, f'(x) shown below. G f'(x) pl B HA F C D E A. H…

A: The graph is given

Q: The relationship between the price and the demand of a certain product is described by the equation…

A: Given price function  p + 0.03x = 143  p = 143 - 0.03x

Q: 1. Determine if the integral is convergent or divergent. If it is convergent, evaluate the integral.…

A: As per the guidelines I am answering 1 question. Nn integral is called convergent if it has finite…

Q: The slope of the tangent line to the parabola y = 2x² + 7x + 7 at the point (4, 67) is: The equation…

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Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A: Topic = Vector

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: 6x2+xy+6y2=13d dx(xn)=nxn-1d dx(constant)=0

Q: Ingrid wants to buy a $15,000 car in 6 years. How much money must she deposit at the end of each…

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Q: SET UP the double integral to find the area of e right by the parabola y = x², on the left by the…

A: Given  Area is bounded by parabola (y=x^2) from right and line x+y=2 from left and y=4 from above

Q: Find the solution of the function 2x = 3x² - 2 by using x = g(x) Method with four decimals accuracy.…

A: The given function is:2x=3x2-2Therefore:f(x)=2x-3x2+2Initial approximation is:x0=0

Q: Determine the intervals on which the function is concave up or down. 1 – 1 t w(t) = +6 (Give your…

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Q: If f(x₁) 0 and f(x₁) > 0 then f has a A at x₁. If f¹(x₂) = 0 and f11(x) < 0, then f has a A at x₂. =

A: As per second derivative test:   If f'(a)=0 and f''(a)&gt;0 then f has a local minimum at x=a.   If…

Q: A company operates two plants which manufacture the same item and whose total cost functions are…

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Q: Suppose that f(x) = √3+e. Find ƒ' (2). f'(2) =

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Q: Determine algebraically the solution to the system:  x^2 + 2y^2 = 11 3x^2 - 2y^2 = 25

A: Solutions are : (3,1),(3,-1),(-3,1) &amp;(-3,-1) For detail...go through the solution...I have…

Q: (d) 4x²y" + y = 0, (e) y" + 16y = 0, Y₁ = √√x ln x Yı Y₁ = cos(4x)

A: see below the answer and calculation

Q: Let f(t) = (t² + 4t+6) (7t² + 3). Find f' (t). f' (t) Find f'(3). f' (3) =

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