Find dy dx 5. = sec ¹(log 7x) y =

Q: 3. Find the solution of the following systems of differential equatio (c) [x' (t) = -6x (t) + 4y(t)…

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Q: Find the angle between the vectors. (Round your answer to the nearest degree.) a =j+ k, b = i +4j -…

A: Given a=j+k b=i+4j-2k

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Q: 6. S²2 (+1/12 - √x) dx

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Q: Find the volume of the solid generated by revolving about the line y = 0 the area bounded by x + y =…

A: We know that if the area bounded by the curve y=f(x) , the line x=a and x=b and X axis , is rotated…

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A: Given that,

Q: Determine if there are any inflexions on the graph given by y=2x4-3x³+ x²+6. Proof they are points…

A: The given function y=2x4-3x3+x2+6

Q: Find the derivative dy dx dx of the function y = sec (1 + 4 + sin ¹(4 + ²)

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Q: Use the row method or column method (as appropriate) to find the first column of BA. 6 -1 5 A = 3 4…

A: We need to find first column of BA.

Q: Find the volume of the solid bounded below by the circular paraboloid z = z² + y² and above by the…

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Q: Verify that f has an inverse function. Then use the function f and the given real number a to find…

A: The given function f(x)=x-9, x>9

Q: 3 4 3η ΣΣ (+1) j=1 k=0

A: A detailed solution is given below.

Q: Solve for x accurate to three (3) decimal places ex-12=7

A: The given equation is  ex-12 = 7  Solve for x.

Q: Obtain the TSE of f(x) = 2x² in powers of (x-1)

A: To Find: The Taylor Series expansion of function 2x-2 with center x=1

Q: For each of the transfer functions below, find the exact response of each system to a step input,…

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Q: 5. 5 S x ³e x² dx

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Q: Find the area of the region enclosed by the circle r = 16 sin θ.

A: A detailed solution is given below.

Q: >dt CD Stat, cosat, 4trat

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Q: Find the solution to the differential equation dz/dt=7te^(5z) that passes through the origin.

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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: = 0? 5. Which of the following is a normal vector to the plane Z = a. C. n = (1,1,0) 72 = = (0,1,0)…

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Q: Find the limit as t-➜0 of r(t)=

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Q: X hat is the value of lima f(a)-aƒ(x)? r-a

A: Topic:- limits

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 8,…

A: Given g(x) is the inverse function of f(x)

Q: 1. Sv 2x - x² dx

A: ∫ un du = un+1n+1+C ∫ cos(ax) dx =sin(ax)a+C

Q: (a) Find if x² + y² + xy =1 dy dx (b) Identify the nature of the stationary points of y=4x³ - 21x²…

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Q: The rate in which the balance of an account that is increasing is given by A'(t)=375e^(0.025t).…

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Q: -2, if x < -1 f(x) = (x + 1, if x ≥ −1

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Q: Find the distance between the points. (−14, 1), (1, −7)                     units

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Q: 2. A plane is defined by the equation 2x - 5y = 0. a. What is a normal vector to this plane? b.…

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Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Each side of a square is increasing at a rate of 6 cm/s. To determine the rate at which the area of…

Q: 5sec 5 sec 5x tan 5x dx

A: Given, ∫5sec 5x sec 5x tan 5x dx

Q: 7. Sara wants to show that (a × b) × ê ‡ à × (b × c). Yasmina says that it is impossible and comes…

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Q: Let f(x) = 4x²(x-8) + 14. Find the critical points c that correspond to local minima. (Use symbolic…

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Q: (2)√√2x+1 dx

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Q: 옻 sin 8x lim X→0 X K X f(x) -0.1 -0.01 -0.001 0.001 0.01 0.1

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

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Q: 4 fsin 2xcos²2xdx

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Q: In the Taylor series expansion of e* about x = 2, the coefficient of (x - 2)4¹ is (a) 24 (b) 4! (c)…

A: Taylor series of function fx at a is defined as:…

Q: 2 0 ¹³² [², [²³² ²² dz dy da. SIL Question 2. Evaluate the following integral

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Q: 4. [ε (8x − 3) (4x² – 3x) * dx

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Q: 16 + x² dx, x = 4 tan(0)

A: Bn

Q: Use linear approximation, i.e. the tangent line, to approximate 101 as follows: Let f(x) = = and…

A: We need to find value using linear approximation.

Q: Figure out the generated volume of rotation the region surrounded by = 4x² and y=4x about X-axis.

A: find intersection point

Q: ind the indicated partial derivatives of the function. (a) f(x,y,z) = xy + 2yz +3zx+xª; ƒx‚ ƒy [(b)…

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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: Find a formula for the quadratic function whose graph is shown. y X 15 f(x) = -5 30 20 10 f 5 (5,2)…

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Q: Find the x-value of all points where the function below has any relative extrema. Find the value(s)…

A: Solution is here

Q: . Determine if AABC is a right-angled triangle, given A(1, 6, −2), B(2, 5, 3), and C(5, 3, 2).

A: Find the squares of all the sides of the triangle and then observe them

Q: so ne dx

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