6. J 4 x4-1 -dx

Q: Find the power series representation of the following functions 3x (a) f(x) = 2x+7

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Q: Find the indicated limit by using the limits lim (x,y) → (a, b) [f(x, y) - g(x, y)] lim (x, y) → (a,…

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Q: E. (DERIVATIVES OF TRIGONOMETRIC FUNCTIONS) 1. If f(x) = secx + 3 csc r, then 2. If g(x) = x² sinx -…

A: To find the derivatives of the following functions.1 fx=sec x+3 csc x2 gx=x2 sin x-3x cos x+5 sin x

Q: Evaluate the following integral using the fundamental theorem of calculus. Sketch the graph of the…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 4xyz + 6yz²…

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Q: S cscycoty 1+cacy dy Select one: OA. - In (1+ csc y) + C OB. In (1+ csc y) + C OC. In² (1+ csc y) +…

A: Given problem:-

Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

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Q: (a) √ (cos r - sin r) da (b) / cot² x da

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Q: Use Newton's method to approximate a root of the equation 2 sin(x) = x as follows. 1 be the initial…

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Q: A population, P(t), of wild animals is growing proportionally to a function of the initial size, and…

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Q: (a) [2 2 2x dx

A: Note: As all are different questions, as per our company guidelines we are supposed the answer the…

Q: Б 2 dv v2.+ 6v - 7

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Q: Find the Taylor or McLaurin series for the following functions f(x) = = x a=0 - 2x "

A: We have to find the McLaurin series for the given function.

Q: The Doyle Log Rule is one of several methods used to determine the lumber yield of a log (in…

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Q: Use implicit differentiation to find dy/dx. b. Find the slope of the curve at the given point.…

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Q: If f is a differentiable function and ƒ"(x)=x4+2x³− 15x², then f has an inflection point at

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Q: Question 4 Find r'(t) given the following vector function. r(t) = 2/³i+34j+37²k O r'(t) =…

A: We have to find out derivative

Q: lim X-00 X *3)* X 1 1+

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Q: Question 12 a)! Let C be a curve defined by the vector equation r(t)=. P(32, 52, e³2) Show that the…

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Q: -5 -3 2-1 3+ 1 1 2 4 N -1 B 2- Submit Question ON 4+ 10. -3 Which of the following is true about = 0…

A: Let's find true statement about given graph.

Q: Differentiate implicitly to find dy/dx. ²+ y² - y² = 29 dy dx 11

A: This question is based on implicit differentiation.

Q: Find the area of the triangle with vertices P(1, 3, −5), Q(0,0,0) and R(4, 5, 1). NOTE: Enter the…

A: The objective of the question is determine the area of the given triangle .

Q: Differentiate implicitly to find the first partial derivatives of z. x In(y) + y²z+ z² = 93 дz əx дz…

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Q: Answer the questions for the function f(x) = 3x - 24x³ C УР f'(x) = 12x - 72xX f''(x) = 36x²-144x…

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Q: Solve, finding all solutions in [0,2x). 4cos x + 4sinx=2√√6

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Q: y(y² + 1)dx + x(y² − 1)dy = 0

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Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

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Q: Evaluate the integral -1/4 7x/4 S (sin x + cos x) dx using the fundamental theorem of calculus.…

A: We have to find the area is -π/4 or not.

Q: Find the derivative of the following function. g(x)= 1+cos x / x + sin x

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Q: Differentiate and simplify this function:  e√t^2+t+1 - e-√t^2+t+1

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Q: Farmer Jones and his wife, Dr. Jones, decide to build a fence on their farm. Because Dr. Jones is a…

A: Follow the procedure given below.

Q: Find the exact values of sin 20, cos 20, tan 20 and the quadrant in which 20 lies. tan 0 = sin 20 =…

A: Solution of given question is written in below steps.

Q: Use a sum or difference identity to find the exact value of the expression. 7π 12 sin

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Q: For f(x, y)= e sin(25x), evaluate fy at the point (77, 0). Of,(7,0)=50 O fy(7,0)=0 Of(7,0)=51…

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Q: sider the DE: dy (6x²y² - 10)dx. = the differential equation 1:ss

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Q: Find the solution of the differential equation that satisfies the given initial condition. dp dt 7√…

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Q: 5. Find the volume of the solid formed by rotating the region bounded by the graph of y=1+√x, the…

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Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2. Find the…

A: Given :fx,y,z=lnxy-zx2

Q: The result of the integral is equal to 4 √ = (x − 1)(x + 1) dx

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Q: The rate of change of N is inversely proportional to CSC(x) · N(x), where If N () = 1, and N (5) =…

A: Given: dNdx∝1cscx.N

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: To find the minimum distance from a point to a paraboloid is just to minimize the function…

Q: x³-y²+z³ = 24.

A: F( x,y,z) = exyz f(x) = ∇f = (yzexyz , xz exyz, xy exyz ) λ∇g =  g(x) = 3x2 , g(y) = -3y2 , g(z) =…

Q: Determine whether the geometric series is convergent or divergent. 27 16 9 4+3 + + 4 convergent…

A: By ratio test we first check the series is convergent or divergent Then, we find the sum of…

Q: Solve the following triangle. B = 70°, C = 50°, b = 8 O A (Simplify your answer.) a≈ (Type an…

A: We will use law of sines to solve this question.

Q: 30. Let f: RR and g: R → R be defined by f(x) = 3x + 1 and g(x) = x² - 2. Determine (fog)(2) and…

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Q: dy dx +²y=e*yª dx 4

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Q: Integrate 3+22 Select one: OA. 7Inlxl + OB. 4inlxl + O C. 31nlxl + O D. 5Inlxl + dz + C + C + C + C

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Q: 1. Find the Taylor polynomial p3 centered at a = 7/3 for f(x) = = COS I.

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Q: Answer the following True or False. If 0 < a < b and 1 < c .be 1 then: c b 1 |--L -dx x True O False…

A: Given.

Q: Write 2x (x+1)² constants. completely in the form of partial fractions solving all the unknown + v…

A: Given problem:- Find partial fraction of 2x/(x+1)2