Find the derivative dy dx of the function y = sec +√4+ sin (4+x²) + x²)).

Q: Q3/ solve the differential equation below: 1. ²-3x+2y=0 (Complementary Function)

A: topic- differential equations

Q: Find the area of a parallelogram having the vertices P(1, 1, -1), Q(4, 2, 1), and R(6,3,1) O √13 O…

A: To find the area of a parallelogram having the vertices P1, 1, -1, Q4, 2, 1 and R6, 3, 1.

Q: 1. 2y7y"+12y + 8y = 0

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Q: Prove that √1+i√3+√1-i√3 = √6

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Q: Q1/ Without using L'Hopital rule, find the following limit. x²-x-2 lim 4x²+4x

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Q: For items 1-2, identify the substitution equations and solve the solution for each. (x - 2y + 5) dx…

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Q: For each of the questions below, indicate if the statement is true (T) or false (F). (a) Any…

A: answer  is next step . as per guideline i can only answer 3 question .

Q: Find the area under the curve 4x²-3x+6 between x = -2 and x=3

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Q: 7. y - 5y + 7y" - 5y' + 6y = x² + 3x - 5 Ans: y = C₁e³x + C₂e²x + C3 cos x + C₁ sin x + x² + ²x -…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3 S² 2 (3x+1) dx x-1

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Q: 2. Integrate the function below using Integration by Parts and with 4 lines only (solution +…

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Q: C. Find the volume of the solid generated by revolving the area bounded by the given curves about…

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Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

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Q: 4. f 30x²5x³+3 dx e

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Q: Find the derivative of y = V.

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

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Q: a) Approximate the area under graph (a) of f(x) = 2/x² over the interval [2,6] by computing the area…

A: Area using rectangle

Q: TL 9. The region R = {(x, y): 0 ≤ x ≤ 2, -√√1-(x − 1)² ≤ y ≤ √1 - (x − 1)²} in the transformation x…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

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Q: Evaluate using Trigonometric substitution

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Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: - 13. If u = (4, -9, -1) and v = 4ỉ − 2] + k, determine each of the following: a. u.v f. (2ū+ v) ×…

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Q: 5. A function u(x, y) is defined by u2³-3xy². (a) Show that u is harmonic, i.e. it satisfies…

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Q: Find the equation of the tangent line to the vector function r(t) = (1-2 arctan(t), 3e¹−¹², 4ln(t²…

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Q: Your are driving away from Tampa. Your distance (in miles) away from Tampa x hours after 12:00 noon…

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Q: Q1/Without using L'Hopital rule, find the following limit. lim

A: We can solve the question as below and as per the asked method.

Q: The Bradford family wants to establish an ongoing scholarship award at a college. Each year in June…

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Q: f21 csc 3xcot3xdx

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Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by 3 L(x,y) = x²…

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Q: Consider the following: (5/2,1), (-9/2, 8/3) Find the distance between these points.

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Q: 2.(D5 – 2D³ – 2D² – 3D — 2) y - - = 0

A: To solve the higher order differential equation.

Q: The figure below shows J(a) and its local linearization at a = What is the value of a? a = 2 What is…

A: linearization

Q: Show that the points form the vertices of the polygon. right triangle: (−4, 5), (0, 7), (2, 3)…

A: The given points are -4,5, 0,7, 2,3

Q: ✓1 - cos e de

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Q: + R (+) et sinti-etcost] a) Find the velocity and acceleration vectors. 6.) Find the speed,…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 13 X ƒ(x) = [5,-3],ƒ(c) = -1/ x²-4,

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Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: Please explain this process: 49 7.760 Σ 7+1 10⁰ 49 = 3 1-7 3 10 ↑ n= P 16.33

A: Using geometry series

Q: Find the derivative of the function using the chain rule. y = log10(7x)

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Q: • Let I be a vector-valued function defined by &(t)= it tal [ouve It cosnt 3-√61-62 12(1-2)' Int if…

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Q: All exponential functions can be written in many forms. Write the function -0.08t f(t) = 340e- in…

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Q: Evaluate the difference quotient f(a + h) - f(a) / h for the function f(x) = x ^ 2 + 4x - 5

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Q: III. Solve the following problems. 1. A manufacturer of tin boxes wishes to make open boxes from…

A: A manufacturer of tin boxes wishes to make open boxes from pieces of tin withdimensions 8 in. by 15…

Q: . A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

A: . A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

Q: 3 S₁ x ³ exdx

A: Evaluate the definite integral :        ∫01x3exdx

Q: Evaluate € fff.₂²². e² dV where E is enclosed by the paraboloid z = 3 + z² + y², the cylinder z² +…

A: We need to find integral.

Q: Which of the following describes the graph of the polar equation r = 2 − 4 cos θ? (a) A limacon…

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Q: its not 1

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Q: Determine the antiderivatives of the following functions: 4. f(3x² +1)4 x dx 5. s dx

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Q: Find the radius of convergence of the power series. (If you need to use oo or -00, enter INFINITY or…

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