2x - 5y = 7 3x + 2y = 4

Q: Let f(t) be the function 2t² + 1t+5. Follow the steps below to use the formal definition of the…

A: Let  be the function .By using the formal definition of the derivative .

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Q: Solve the initial value problem If the solution is y = co + C₁x + ₂x² + C3x³ + C4x² + C5x5 +C6x6 +…

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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: dy dx = 2 2 Cosy

A: Given that expression we have to find general solution

Q: 3. Use the definition of Taylor series to find the Taylor series centered at a = 1 for f(x) = ln x

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Q: 4 Find all critical numbers of fa)=x² (x-23

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Q: Evaluate the limit lim x →0 O -1 1 18 1 9 √81-x-9 X

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Q: 14. A rectangle has its base on the x-axis and its upper two vertices on the parabola y =12-x². What…

A: The second derivative test states thatWe use this to solve the given problem.

Q: Derive the formula of a circle using horizontal strip

A: We need to derive the formula of the area of a circle by using horizontal strip

Q: What are the coordinates of the vertex of the equation (+8)² (x+2)² 36 = 1? 25 O (-2,-2), (-2, 14) O…

A: The given equation is

Q: ¡¡¡ ³² 2 cos (x²) 0 0 4у Evaluate the integral 2 cos (x²) 00 4y 5√√Z (Type an exact answer.) -dx dy…

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Q: In a large city, the road system is set up like a Cartesian plane, where streets are indicated by…

A: Given that in a large city, the road system is set up like a Cartesian plane, where streets are…

Q: A = 90°, B= 20°, a = 7;

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Q: What is the limit of (Cos(x)-1)/x^2 as x approaches 0?

A: Given that the expression we have to find the limit as x approaches 0

Q: ellipse: ² + ² = 1 4 Given the ellipse: (a) Find the coordinates of the center of the ellipse (a)…

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Q: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 6 m, at what…

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Q: A1. Milk or meat production Y per day is best explained by the inputs: feed needed per day in kg,…

A: The objective of this question is to determine the Lagrangian, find the First Order Conditions…

Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

Q: Can you please answer question e and g?

A: e) From the graph it is clear that:LHL = Left hand limit at x=3: limx→3− f(x) = -4RHL= Right hand…

Q: (t²-2t)³ 5t 4. The voltage applied to a 0.25-F capacitor is given by v=- 3.7 s. . Find the current…

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Q: Estimate the average value of f(x) from x = a to x = b. 28 21 f(x)

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Q: A stone is dropped from the upper observation deck of a tower, 500 m above the ground. (Assume g =…

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Q: In a large city, the road system is set up like a Cartesian plane, where streets are indicated by…

A: The baseball field is located 2 blocks west of street B and 28 blocks north of street A.

Q: Suppose that we're making and selling some widget and the profit (in dollars) when making a widgets…

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Q: -(-²-) - and the point P(-3,0), which lies on the graph of f(x), determine the equation of the…

A: Given the function  and the point , which lies on the graph of , then to determine the equation of…

Q: Find the radius of convergence, R, of the series. R = Σ 5(-1)"nx" n = 1 Find the interval, I, of…

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Q: b) 9-x² x²+4x+4

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Q: Find the slope of the tangent line to the graph of the polar equation at the point specified by the…

A: Given that the polar curve

Q: 56. The length of required to enclose a rectangular field is 3000 meters. What are the dimensions of…

A: Let the length of the rectangular field=x mLet the width of the rectangular field=y mThe figure of…

Q: find the limit if it exists, or show that it does not exist.  lim (x,y)→(0,0) (x^4 −y^4)/x^2+y^2

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Q: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

A: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

Q: The approximate rate of change in the number of design patent applications received in recent years…

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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: Graph the function for one period. =tan(лx/2) for 0.5 1.0 1.5 y y-intercept 1.0 vertical asymptotes…

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Q: For the following exercises, use the Mean Value Theorem and find all points 0 < c < 2 such that ƒ(2)…

A: The given function is,Take derivative.Substitute x=c

Q: Choose the correct graph below OA O OB. Oc W NE

A: The derivative of the downward parabola is the line with a negative slope.The derivative of the…

Q: n = 1 (-1)"x" n

A: Given that the series we have to find the radius of convergence and interval of convergence

Q: Express the function as the sum of a power series by first using partial fractions. (Give your power…

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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: The Taylor series for f(x) = e² at a = 3 is Σen(x − 3)". n=0 Find the first few coefficients. Co C1…

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Q: If sin(-s) = 5/13, and (a) (b) (c) (d) sin s cos(-s) COS S 3πt < s < 2π, compute the following.…

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Q: The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x) = x (20x²…

A: The given marginal profit function , where  is the amount of cheese sold in hundreds of pounds.The…

Q: 2. S x³ +1 x³ - x² da dx

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Q: nn n=0 4"n! η!

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Q: Sketch the graph of ONE function that satisfies, ALL of the following conditions. Label ALL…

A: The given condition to draw a graph of function

Q: √x 4√/2x+1dx X

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Q: sin (2x) = 4 cos(x)

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Q: Determine whether the series converges or diverges. Σ 5 sin (²) n n = 1

A: The given series is

Q: Find an equation of the curve whose tangent line has a slope of f'(x)=x given that the point 1,-…

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