- Find the area between the parabola x² = 4y and the straight line x-2y + 4 = 0

Q: lim cos x x-0 , which among the following should result, in equivalent form, before L'Hopital's Rule…

A: To evaluate: limx→0 cosxx Let y= limx→0 cosxx ⇒y= limx→0 cosx1x

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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Q: dx What is , where dy' x³ + y³ = 3xyusing differentiation? implicit dx dy y-x² y² +x dx y-x y²-x dy…

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Q: 3. fe+tanx+(tan²x)+taxdx

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Q: Find the area of the region bounded above by y = x2 + 8 and below by y = 4. 10- 4 2 X -10 8 6 4/-2…

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Q: The graph of } = xe-r is symmetric with respect to the Origin None of these the x-axis the y-axis

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Q: 8-9 Let A = 2 3 (a) Find 5A +6B. 5A +6B = and B= 9-2 Complete parts a through d.

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Q: Find the general solution of the given differential equation. x²y + xy=5 y(x) = Give the largest…

A: To find the general solution of the given diffrential equation.x2y'+xy=5To give the largest interval…

Q: What is the lim_0+ 2²-In(x) For answers write... that are in decimal form and round off to fractions…

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Q: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

Q: Give the general equation of the plane containing the point (3,-1,4) and perpendicular to the line…

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Q: What is the lim (3)¯ I 7 sec (7x) cos(3x)?

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Q: 2 X * sin² Lys y dy d

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Q: For x² +4²³-1=0, find the targent at (3,-2)

A: We can solve this as follows:

Q: Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph of,…

A: To find the gradient of the tangent line of the point (5,1) on the graph of x+xy+2y2=12 Formulae…

Q: Whatis the derivative of y = sin (2x − 1)? dx = 2 cos (2x - 1) dy dx = cos 2x dy -2 cos (2x - 1) cos…

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Q: 2 dy 67 +13

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Q: What is the lim0+ (=//=²²1)? - If your answer is a Whole Number Fraction (+) Positive Infinity (-)…

A: Let's find limit of the function.

Q: Find the area under the graph of x = 4 - y² on the interval [0, 2]. -3 -2 -1 1 2 3 → 1 0 -1 16 3 16…

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Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

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Q: The revenue in dollars for a product is given by the function R(x) = 36x -0.01x² where x is the…

A: To find average rate of change in revenue as x varies.

Q: For the next three series, (a) determine the radius of convergence, (b) determine for which the…

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Q: Let f denote a piece-wise defined function whose graph on the closed interval [-3,3] is shown below:…

A: f denotes piece wise function .  Identify the interval where function is concave down

Q: For the function f(x) given below, where x > 0, evaluate lim f(x). X18 f(x) = ln(9x³ + 10) - In(2x²…

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Q: The domain for the function y = all real numbers except 3 and 0 ○ {x/x > 3} O less than 3 except 0…

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Q: The temperature of a room in degree Celsius is modeled by a differentiable function T(x) where x is…

A: We need to choose correct option.

Q: A manufacturer has determined that the weekly profit from the sale of x items is given by the…

A: SOLUTION-

Q: Q1: Find the Fourier coefficients and Fourier series of the triangle function f(x) defined by

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Q: Which of the following is equivalent to log₂ (2x²) - log₂ (¹) - log₁(x¹)? Select one alternative: O…

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Q: 3. Choose three vectors: and Use these vectors to verify the associative property.

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Q: Sx² 1 if if > 2 x f(x) = 5 3 if x < 2 af is differentiable at x = = 2 bf is continuous at x = 2 cf…

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Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = . √3 2…

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Q: Assume x and y are functions of a third variable t. If xy = 20 and d = 10, find dy dt dt x = 4.…

A: u.v = uddx v + v

Q: Evaluate the following integrals. (a) (b) Sx√4 x√4 + x² dx

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Q: A 1 lb sponge initially contains 5 lb of water. As it is lifted up from the ground, the sponge loses…

A: Answer is option d here decrement in water is linearly (as constant rate)

Q: 2. Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1. 2

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Q: dx What is where dy' 3 x³ + y³ = 3xyusing implicit differentiation? dx y- dy dx = dy y²_ dx y+x² =…

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Q: The following table shows the rate of water flow (in L/min) through a dam. t (min) 15 9 13 17 21 25…

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Q: ] Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

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Q: 5. Identify and sketch the graph of y = x² + 1 in R³. M

A: y=x^2+1 x=0 y=1 x -3 -2 -1 0 1 2 y 10 5 2 0 2 5

Q: 4.z=(y'-2) 3/4-2y ;z= dz dy

A: See the details solution in below

Q: Instruction: Evaluate the following Integrals. Write your COMPLETE solutions neatly and organized.…

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Q: Find the area under the graph y = x 3 on the interval [1, 8]. 1 2 3 4 5 6 7 8 9 -NW 01 5- 4 3 2 क्त…

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 - 8x² + 2 (a) Find…

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Q: 2.) Find the volume of the solid generated by rotating the region enclosed by y = x + 3, y = 0, x =…

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Q: Solve the following initial value problem using Laplace transforms. d² y dt² -9y=4e³¹; y (0) = 0,…

A: d2y/dt2 - 9y =4e3t; y(0)=0, y'(0)=-1.

Q: Evaluate the limit: Lim X--3 (2-√x² +100 x + 3

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Q: Evaluate: lime 1-sin 8+cos 8 sin 20-cos 0

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Q: -i+3j and Y = 4i - 2j + 2k. -Y. 3. Consider the vectors X and Y in R³ where X Find the unit vector…

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Q: y=xe

A: As per the company guidelines we can solve first question. I hope that the given solution will help…