Without evaluating integral, prove that 1 dx S 0 /2+x-x² 2 < 1 √2

Q: Convert the general form to standard form of parabola

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Q: d the polar coordinates if (x, y) = (-√3, 1), r≥ 0, -2π < E

A: Given query is to find the polar coordinates.

Q: O TRIGONOMETRIC IDENTITIES AND EQUATIONS Proving an identity using fundamental trigonometric…

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Q: Find the first partial derivatives of the function f(x, y) = ln (x + √√x² + y² 1. fx(3, 4) = 2.…

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Q: * 36, got 6=-8, 311/2<0² 2π1₁ eSC

A: given cot(∅)=-8tan(∅)=1cot(∅)=-18∅=tan-1-18∅=352.8749837o

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. tan(x) y =…

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Q: (5) Determine if the alternating series converges Σ(-1)^n. 8 n=2

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Q: The limit lim X-8 √9x² – 1 3x − 6 Select one: O True O False = 1 Ignore "Give your reasons" below.…

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Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

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Q: If ƒ(x) = (x² + 4x + 5)², then f'(x) = 4x³ + 24x² +52x + 40 f'(2) =

A: Given f(x)=(x²+4x+5)²

Q: e¹ = 7

A: Given query is to find the value of t.

Q: Let F(x, y) = (x + y, x²), and let 7(t) be the parameterization of the line segment from (0, 4) to…

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Q: Let Find A -1. if it exists. 4) b) O ) O 05/13/1 1 ۔ ه - -4 0 0 -1 | | ON T مام دام نه دانه شبانه…

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Q: the rectangular equation if r = 4 cos 0 + 4 sin 0

A: Given query is is to find the rectangular equation.

Q: (1) Use the Limit Comparison Test to determine if the series is convergent. η3 1 Σ+2 n=3 .

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Q: 2) Solve the given Variable separable DE 1) x cos² y dx + tany dy =0

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Q: Remove arbitrary constant in the given relation. x = sin (w t + ß); w - parameter, not to be removed

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Q: Find y' if x = y*. C Note: Leave your answer in terms of ï and y. y

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. = $₁²04²…

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Q: The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of…

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Q: Question 1 [ a) [ b). Consider the function f(x)=x²+3x+c Find the domain of f(x) in terms of c on…

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Q: A company's marginal cost function is  MC = 10x3/2 − 20x2/3 + 1,  where x is the number of units,…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: We need to find out the amount of paint that is needed to apply.

Q: Find equations of the tangent line and normal line to the curve at the given point. y = x4 + 5ex,…

A: To find the equations of the tangent line and normal line to the curve at the given point.y=x4+5ex,…

Q: Sin 0=4/5 Find a g 1/5 where 40 < x 180

A: sinθ=45⇒θ=arcsin45+2πn, θ=π-arcsin45+2πn⇒θ=53.13∘ +360∘ n, θ=126.87∘ +360∘ n

Q: Use Laplace transforms to solve the initial value problem: y" - 10y' +9y = 5t, y(0)=−1, y'(0) = 2

A: By using Laplace transforms to solve the initial value problem.y''-10y'+9y=5t, y0=-1, y'0=2

Q: eah expressi 36 Si=1/3180° < 0 <3·10° 0 ter 0 312=80 Simplify 3

A: Given that:sinϕ=-13 ;           180°&lt;ϕ&lt;270°

Q: Given the function below ✓-45x³ + 72 Find the equation of the tangent line to the graph of the…

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Q: Determine two coterminal angles tive and one negative) for 2 a) += π 8 1. +- and انت انت -4-2 T and…

A: To determine two coterminal angles one positive and one negative for the following angle.+23π

Q: 1. (a) (b) (c) (d) Find Maclaurin series for the function e-2x 2² 2³ 1+2x-x + _ 2! 22 2x+x 3! 1-2x²…

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Q: A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is…

A: The given data is: If the trough is being filled with water at the rate of 0.1 m3/min dVdt=0.1m3/min…

Q: If r²y - 12y, calculate dy dr using implicit differentiation.

A: According to company rules.. I need to solve first question... Please repost second question

Q: Use a trigonometric identity to evaluate the integral. [tan²(x) dx = +C

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Q: 21. Find the volume of the solid bounded above by the surface z = ryery and below by the rectangle…

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Q: If ƒ(6) = 7 and ƒ’(6) = 4, estimate ƒ(5.8). f(5.8) ~

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Q: Given f is a differentiable function such that f(4) = 2 and f'(4) = -3. If g(x) = 2x3 * f(x), find…

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Q: Express the angle -150° in rad 1. 2. - 6. 5 1|32|2N|LA 6 3. 4. None of these 5. 11 6 k 11 7T kgk k…

A: We have to change in radian form from the given degree

Q: Approximate the area under the curve graphed below from x = 2 to x = 5 using a Right Endpoint…

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Q: Let z = 6ex²y³. Then: дz дх дz ду

A: We can solve this as follows:

Q: Use technology to obtain approximate solutions graphically. All solutions should be accurate to one…

A: NOTE: Refresh your page if you can't see any equations. . line-1 passes through points (0,1) and…

Q: 16. Determine lim f(x) if the given function is x→2 f(x) = 2.², 82r, if if x 2 x

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Q: Q3.4 You have been given the Solve it and write function of x. Your youtu wer innitial value problem…

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Q: Perform the subtraction. E4816-C8416 E4816-C841616 (Simplify your answer.)

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Q: Complete the table by finding the balance A when P dollars is invested at rater for t years and…

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Q: (c) Find the value of √a²- [₁ 2(x+y) x² + y² giving your answer in terms of a. 1+ dx dy,

A: The given integral is  ∫0a2-x2∫-aa 1+2(x+y)x2+y2dx dy

Q: lim x -> 0 (3x * cot(3x)) . Do not use sing L'hospitals Rule

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Q: Find the curvature by using the formula k(t) = (a) r(t) = (e¹²¹)i +213 +4k at the point where t = 0…

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Q: Find a parabola with equation y = ax² + bx + c that has slope 10 at x = 1, slope -14 at x = -1, and…

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Q: Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and…

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Q: 2. Suppose that f(1) = 2, f(4) = 7, f '(1) = 5, f '(4) = 3, and f" is continuous. Find the value of…

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