Algebraically prove the identity, Left Side sin +1 1 sin 8-1 2 sec² 0. Right Side

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² =…

A: Let's find surface area rotated about x=0.

Q: The height of a certain amusement park ride follows the function h(t) = −³+ 11t² — 32t + 28, where…

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Q: A rectangular field is to be enclosed with a fence. The available fencing material is 150 meters…

A: This is  a problem related to maxima and minima of the function. Based on the general formula and…

Q: 4. Find the Taylor series for f(x) = ln(1 + x) centered at a = 3. Give the first 5 terms of the…

A: This is a problem related to taylor series expansion. Based on the general formula and concept we…

Q: A curve is defined by the parametric equations Find the length of the curve from t=1 to the closest…

A: .We have to find the length of curve,

Q: d. What are the intervals of concavity? e. What are the x and y-intercepts? f. Are there any…

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Q: Which of the following statements is (are) true? I. If f is a function from [a, b] to R and F is any…

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Q: Suppose you are given a square with an inscribed circle as shown below. If the area of the square is…

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Q: dx √3 1 + x²

A: we use the  formula ∫dx1+x2 = tan-1 x    +C

Q: 5. Find the residues of the following: a. 2-2 z(1-2) at z = 0; at z = 1

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Q: Farmer Brown had ducks and cows. One day she noticed that the animals had a total of 12 heads and 42…

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Q: Solve for y esec(4y²-6y+14) = 3x + 1

A: To find the value of y , first, we take the logarithm on both sides of the given equation and then…

Q: The sum of two integers is 12. If the sum of 4 times the square of the smaller integer and 8 times…

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Q: 6dx x - √ S 3√x²

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Q: kample 8: Find the point where the line = 1 + t, y = 2t, and z = -3t intersects the plane - 4x+2y-4z…

A: Topic:- geometry

Q: Making a suitable change of variable and modifying accordingly the limits of integration, calculate…

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 lny [TD [t ex+y dxdy

A: Given problem:-

Q: Problem 7. Find absolute extreme values for f(x) = ³ − 6x² + 5, x € [1,5].

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Q: 3. Find the general antiderivative of f(x) = x² + 3x+4 sinx.

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Q: A family has a monthly income of $4052. Their monthly expenditures are as shown in the graph below.…

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Q: Find the Volume: Rotate the region bounded by y = 7-x², x=-2 and x = 2 and the x-axis about the…

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Q: dy dx If y = (sin x)¹/, then (sin x) ¹/x In(sin x) x² (sin x) ¹/x x - ln(sin x) x² x cotx - In(sin…

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Q: Consider the initial value problem y + y = 8 + 2 cos 2t, y(0) = 4 a) Find the solution of this…

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Q: 120 N. if the distance between th charges is doubled, the force will be; O 15 N O 30N 60 N O40N

A: We will solve the problem.

Q: 5. Two lines have equations: L₁: x = 3t + 1, y = 3, z = −t + 2, teR and L₂: x = 2s +3, y = −s + 1, z…

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Q: 2) Find the particular solution using the following indicated initial values. (D² +4D+5)y=10e³; when…

A: Given :D2+4D+5y=10e-3x

Q: Find the Volume: Rotate the region bounded by x = y²-6y + 10 and x = 5 about the y-axis

A: A detailed solution is given below.

Q: dy For the following composite function, find an inner function u = g(x) and an outer function y = f…

A: We need to find derivative.

Q: Nx - My If = R, where R is a function depending only on the quantity z = xy, then the differential…

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Q: KIN KIN 0 2 d2 sinr do dr dọ

A: A detailed solution is given below.

Q: II. Solve the initial value problems given the following: dy 2 if y(-1) = 21. = -2x + 3x dx dy -2x…

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Q: Which interval notation represents -3 ≤x≤3? 1) [-3,3] 2) (-3,3] 3) [-3,3) (-3,3) 4) 1 O O O O a b n…

A: From the convention of interval notation, We can write: a≤x≤b  as x∈[a,b] which represents x which…

Q: Solve the systems of equations by using the matrix inverse method. r+s+t+w=4 2r-s+w=2 3r+s-t-w=2…

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Q: 3 50 times داد + 33 u س اع

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Q: The expression f(x+h)-f(x) h for h#0 is called the difference quotient. Find and simplify the…

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Q: During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s…

A: According to the company policy we are supposed to answer only first three sub parts and rest of the…

Q: 10. The expression sin (32) cos (22) - cos (32) sin (22) is equal to

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Q: 3. Find the intersection of the following planes: ( x - 3y - 2z =- 9 == 2x - 5y + z = 3 3x + 6y + 2z…

A: We have to find the intersection of 3 planes.

Q: f(x)=x2-3,P(4,13) a.find mtan b. Determine an equation of the tangent line at P. c. Plot the graph…

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Q: The area of an equilateral triangle with sides of length x is given by the function √3 defined by…

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Q: (a) In the accompanying figure, the area of the triangle ABC can be expressed as area ABC-area…

A: Let's solve for area of the triangle.

Q: A boat on the ocean is 2 mi from the nearest point on a straight shoreline; that point is 9 mi from…

A: Concept: We have a boat on the water, and let the closest point on a straight shoreline be x, In…

Q: Q4- Solve the following differential equation: (1 + x²) dy + (y - tan-¹(x)) dx

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Q: 1 Consider the function f (x) = on the interval X - 1, 1]. If the Mean Value Theorem can be applied…

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Q: 0 KIN KIN π 2 2 ²/² 02 sin o dr do de 0

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Q: Question 8 Evaluate: lim-1 (3-22)tan (7). e 3m 01 O None of the choices O e

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Q: …... VOIN'I Select the correct choice below and fill in any answer boxes within your choice. O A.…

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Q: solution = Give the ODE : general x" + 3x² - 4x of the following

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Q: √√3 ल dx 1 + x 2

A: The given integral is 1/(1+x2) limit from sqrt(3) to sqrt(3)/3.

Q: An angle co-terminal to 19 6 11m 6 is

A: Given query is to find coterminal angle.