Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule), estimate the area under the graph of the following function, using two and then four rectangles. y=1-x² between x = − 1 and x = 1

Q: Determine whether Σ(-1)^-1 is convergent. 1 √n +3 n=1 rk in order to roccio full in utiol onadit

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Q: Find the area between the curves f(x): 3x² 12 (in dark blue) and g(x) = -x² + 4 (in dark red) over…

A: Region is bounded by f(x)=3x2−12 and g(x)=−x2+4 over the interval [−3,3]

Q: Evaluate this integral | √2 3 (1+x) + C √x(1 + x² ) 5 dx (1+x)³ +C 3 ○ 2 √ (1 + x ³ ) 6 + C Va 3 6 3…

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Q: es. [Assume that f has a power series expansion. Do not show that R₁(x) → 0.]

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Q: Use the ratio test to determine whether an+1 lim n→∞ an (a) Find the ratio of successive terms.…

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Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min.…

A: A circle has an initial radius of 50 ftr=50 ftRadius begins decreasing at the rate of 4…

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Q: A commercial cherry grower estimates from past records that if 16 trees are planted per acre, then…

A: To find the maximum yield.

Q: 3+x 4. (a) Find a power series representation for the function f(x) = is the radius of convergence?…

A: The given function is

Q: Tutorial Exercise Consider the given function. f(x) = c² +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2,…

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Q: The total cost in dollars to produce q units of a product is C(q). Fixed costs are $14,000. The…

A: The total cost in dollars to produce q units of a product is C(q)Fixed costs are $14,000

Q: Part: 0/2 Part 1 of 2 The domain offis Given that the domain of a one-to-one function fis [-3, -1]…

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Q: 4. Find the first five terms of the binomial series for f(x) = √√1 + x

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Q: Consider the function f(x) = x³ + 6x² - 16x - 104. = A. Verify that f(x) Theorem on [4, 5]. ³+ 6x²…

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Q: 1 S² F(x) '9 +6² f(x) dx = 37 and g(x) dx= 18, find I' [3f(x) + 5g(x)] dx.

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Q: Solve the given differential equation. 3x²y" +6xy' + y = 0

A: To solve the following differential equation.

Q: Evaluate Hint: Using power series. lim x-0 -32-³ -1+3x³ - 2/x6 13x⁹

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Q: Solve the following integration :- 3 S sin³x Sin³x cośx dx

A: The given integration is

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Q: Use the following function to answer this question ; f(x)=sqrtx+7, g(x)=2x+4, h(x)=x/2   a/…

A: Use the following function to answer this question ; f(x)=sqrtx+7, g(x)=2x+4, h(x)=x/2

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Q: 2. Consider the following three points (a) (b) ( (c) P= (1, -3,1), Q = (2, 1,0), R= (1,0,1) Find the…

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Q: dy Find and dx d²y dx² x = e¹, y = te-t dy dx d²y dx² For which values of t is the curve concave…

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Q: Solve Cauchy problem for the non-homogeneous equation: 4 y" +4y' + 3y = 3x, y(0) = − ½, y'(0) = ²

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Q: Use the parametric equations of an ellipse,x=6cos(θ),  y=3sin(θ),  0≤θ≤2π,to find the area that it…

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Q: Find the two solutions of the given equation z² + 6z+ 10 = 0. / in your answers should be positive Z…

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Q: * Find dy dx = the general Solution of :- - X+3x2 √x² + 2x³² 2

A: We use the variable separable method to solve the given differential equation.

Q: If 6400cm2 of material is available to make a box with a square base and an open top, find the…

A: If 6400 cm2 of material is available to make a box with a square base and an open top,then to find…

Q: A = 90°, B= 20°, a = 7;

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Q: Let P(t) represent the number of grizzly bears in a population at time t years, when t ≥ 0. The…

A: P(t) is increasing at a rate directly proportional to 600-P(t)P(0)=400

Q: Set up the iterated integral for evaluating f(r,0,2) r dz dr de over the region D, where D is the…

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Q: Let f" (x) = 6x - sin x. ƒ' (0) = 1, f(0) = 2. Find f(x) ○ x³ O x³ + sin x + 2 ○ x³ – sin x + 2 ○ x³…

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Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

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Q: * Find the general Solution of dy dx = 4. x² ln x

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Q: Let z = 9.8 - 5i. Write z in the form a + b*i: Z = 9.8+5*i Let u = 5 - 2i and v= - 8 + 6i. Write u +…

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Q: Take the logarithm of both sides of the equation and expand it using the product rule of logarithms…

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Q: What substitution(s) would make the following integral simpler? I.e., simple enough to integrate by…

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Q: If what does the following integral equal? 17 |_ * = [9f(x) + 3g(x) − h(x)]dx · - 50 - 17 - 50 - 17…

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

Q: Find the slope of the tangent line to the parametric curve 3 cos (t) (y = 2 sin(t) X = at the point…

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Q: use € Calcus implicit different to find sy ldx Q32 y cos (ty) = 2x + 2y

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Q: Use the information given below to find sin(a-B). tan a = with a in quadrant 1 12 5' sinB =15, with…

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Q: Find the area between the curves f(x) = 3x² + 12x − 15 (in dark blue) and g(x) = -x² - 4x + 5 (in…

A: We need to find area between the enclosed curves.The formula we will use is given by -

Q: For 0 ≤ t ≤ 30, the rate of change of the number of mosquitoes on Tropical Island at time t days is…

A: The objective of this question is to find the number of mosquitoes on Tropical Island at time t=30…

Q: cos(3x) = ² √2 2

A: Given that expression we have to find a solution