STRUCTIONS: Differentiat respect to x) using any method. (x) = √x + 2x X _x) = x sin-¹(x)

Q: Use integration by parts to evaluate the following integral. 1 12 S 0 x In 12x dx

A: Given integral:- ∫0112xln12xdx

Q: Solve the differential equation. (9 + tan y)y' = x² + 9

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Q: Consider a third-degree polynomial f(x), which has the properties f'(1) = 0, f'(3) = 0. Can there be…

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Q: Use spherical coordinates to calculate the triple integral of 1 x² + y² + z² f(x, y, z) = over the…

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Q: (2,-4) (0,-6) . Assuming that f(x) is of the form A · Bª, write an expression for f(x): f(x) =

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Q: Fill in the blank. The One-to-One Property of exponents with natural base e states that if ex = ey,…

A: Given that  e(x)=e(y) ex=eyThe one to one property of exponent states that is base is same then…

Q: 2. Consider the function f(x) = (2x³5x + 1) (3x² − 4). A. Distribute out the product of the two…

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Q: Each side of a square is increasing at a rate of 2 cm/s. At what rate (in cm^2/s) is the area of the…

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Q: 12. Find the area of the region bounded by the graphs of f(x) = sin x and g(x): = cos x, for π/4 ≤ x…

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Q: Find all the first and second order partial derivatives of f(x, y) = -7 sin(2x + y) + 5 cos(x - y).…

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Q: Section 7.1 Problem A Differentiate the power series representation of f(x) Section 7.1 Problem B =…

A: Please see the below picture for detailed solution.

Q: If r(x) x-intercept(s) = x+4 x²-4 ,find the following: a. b. y-intercept c. Vertical asymptote(s),…

A: given function is  rx=x+4x2-4

Q: Integrating factor of dy -5 y=e³t t dt is µ(t)= 1 Select one: O True O False

A: Divide rhe equation by t and then go ahead

Q: LIM x to 09 tanh(x)/tan(x) using the L'hospital's rule

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Q: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

A: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

Q: Find the point on the curve r(t) = (5 sin t)i + (-5 cos t)j-12tk at a distance 26 units along the…

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Q: In order to solve the following Bernoulli's equation dy dx we use the substitution e+3 Select one:…

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Q: Express the location of 7, 2πT ,6), given in cylindrical coordinates, as an exact answer in…

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Q: Use the graph below to determine the equation of the circle in (a) center-radius form and (b)…

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Q: Find the local linear approximation of the function f(x)= square root of (1+x) at x0=15, and use it…

A: Linear approximation at x = a, L(x) = f(a) + f'(a) (x -a)  Therefore, the linear approximation of…

Q: A cable runs along the wall from C to P at a cost of $5 per meter, and straight from P to M at a…

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Q: 1. The graph below shows the function f(x) = 3(2)*. a. Where is f(x) increasing? Explain. b.…

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Q: 5- find a, b and C if w= a.tan (x²+1)_baxy + cryin (z) t-2 and Z=2t²_ze 2 x= zt², J = ze wy =…

A: z = 2t2 - 2et-2  At t = 2, z = 8 - 2 = 6 dz/dt = 4t - 2et-2  At t = 2 dz/dt = 8 - 2 = 6 x = zt2  x =…

Q: Find the solution of the differential equation that satisfies the given initial condition. xy' + y =…

A: Given

Q: that has been recently. There is a been manufactured. The temperature is represented by T (t). the…

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Q: Find the partial derivatives indicated Assume the variables are restricted to a domain on which the…

A: zx : hold "y" constant -- treat it as a known constant, letting only x be a variable. zy: hold "x"…

Q: = 1 y' + ²y = ∙y' + a) Is the given differential equation nonlinear? Is it a Bernoulli's equation?…

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Q: 9. f 6 sec¹ xdx

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Q: Evaluate Your Answer: Answer [₁¹ 1 - 3x √x dx

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Q: 256√√3 4-52.4 4√√2 3 - ANZ 20

A: Topic:- application of integration

Q: Find the partial derivatives of the function fz(x, y) fy(x, y) fay(x, y) fyr (x, y) = f(x, y) =…

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Q: (2,-4) (0,-6) Assuming that f(x) is of the form A. Ba, write an expression for f(x): f(x) = 0

A: We see that the graph passes through two given points. We will substitute the points on the function…

Q: Find the positive integer that minimizes the sum of the number and its reciprocal.

A: Let the positive integer is x ( x > 0) The sum of the number and its reciprocal is f(x)  (let),…

Q: Find an equation of the slant asymptote of the curve 4x³10x² 11x + 1 x² – 3x y = =

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Q: (5y²+3 x)dx+7 xydy=0 (*) a) Determine whether the given differential equation (*) is exact SM-Nx -dx…

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Q: Evaluate Definite Integral √x ³² (2x² + 1) ªdx 2.

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Q: Use what you have learned in Calculus II to find the area of the triangle made up of the points…

A: Let's find area of hexagon.

Q: Evaluate the repeated integral: a) 0 12 e² - 12 e b) 06 c) 0 24 d) 12 e) 0 24 e² - 24 e f) O None of…

A: We need to find the value of ∫-11∫1y-2∫ee23x+3yzdzdxdy

Q: Help me Solve the following(step by step) a) 3-4|x+3| ≥ 1 b) |x^2| +5=0 c) x^2 +4x=2x+4 d) 6-2x>-x

A: (a).The given inequality is:3-4x+3≥1

Q: Determine the type of DE (select all that applies): (2y3x3) dx + 3xy2dy=0 Exact Linear None of these…

A: DE

Q: Find indicated rate of number 3

A: Topic:- application of derivatives

Q: If f(x, y, z) = xe² sin (42), then the gradient is Vf(x, y, z) =

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Q: city of Pittsburgh. The Revenue function R(q) for the program was given by: -0.00381q² + 62.476q 100…

A: Formula for average rate of change

Q: Question 2 Consider the point P(2,-1,-4) and the vectors a = and b= (a) Find the unit vector u that…

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Q: 1. Consider the expression √2+√√2+ √2+ √2+.... (a) The recursive sequence an+1 = √2+ an with ao = √2…

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Q: If a rock is thrown upward on the planet Mars with a velocity of 15 m/s, its height above the ground…

A: Topic - Application of derivatives We are given Height of the rocket after t seconds…

Q: The following differential equation is exact (7x+14y) dy-(8x-7y) dx = 0 Select one: O True O False

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Q: WORK PROBLEMS (. You need to provide a clear and detailed solution for the following Questions: )…

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Q: Find the surface area of revolution about the x-axis of y = 4 sin(7x) over the ㅠ interval 0≤x≤ 7

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Q: lim x to 0 tanh(x)/tan(x) using the L'hospital's rile

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