Use logarithmic differentiation to find the derivative of the function. y = (x5 + 2)²(x4 + 4)4 y'(x) =

Q: What is the partial sum of terms 12 to 15 of the arithmetic sequence 88, 75, 62, 49, ...? O 198 O-45…

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Q: 3. Form a differential equation by eliminating the constants a and b: y = ax² + bx

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Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: Solve the following differential equations of 3x d'y dx² +9y=2e³x +18x+18

A: We need to solve D.E.

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A: Given: x= y2 + 4y, x=0

Q: Evaluate the integral. (Use C for the constant of integration.) √3x√1- 3x√ 1 - x4 dx

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Q: 03: Evaluate the following integrals dx (1) √√₂√x (1+√x)²³ S=

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Q: 1 3 Solve the following differential equations of v\dv: (6x²-y+3)dx+(3y²-x-2) dy

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Q: Suppose that f(x, y) = x +y on the domain D = {(x, y) | 1 ≤ x ≤ 2, x² ≤ y ≤ 4}. D Then the double…

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Q: 2.1 q h(q) 11 0.9 1.2 1.5 1.8 20 35 61 108 Estimate h' (1.5) using the table above. h' (1.5)~

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Q: Solve the following differential equations of d²y dx² +9y=2e³x +18x+18

A: The given differential equation,      d2ydx2+9y=2e3x+18x+18

Q: Question 2. Let f(x, y) = 5xy² + sin(x + y). Find the following: (a) The gradient of f(x, y). (b)…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: Epa is investing $2500 at 6% per annum, with interest compounded continuously. She wants to come up…

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Q: [x√x + 1dx

A: Here we have to integrate I=∫xx+1dx

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A: We have to find the value of IRA.

Q: Evaluate by interperting in terms of area, Find the area 4 I 15x-31dx

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Q: Find dy/dx for the following function:: √y-etanx = 2

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Q: f= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the…

A: Please refer too the image below

Q: A parabola is formed when a plane slices through a cone. Which of the following describes the…

A: Solved below.

Q: A 14-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

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Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: Part 2. Find the Standard Equation 2. circle with center at (4,-5), diameter is 6

A: Standard form of Equation of circle is {(x-h)^2}+{(y-k)^2}=r^2 Where, h,k = center of circle =…

Q: p=q= r= (Simplify your answers, including any radic

A: Follow the procedure given below.

Q: d²y Find dx² x = ² + 2, y = ² + 7t dy dx d²y dx² For which values of t is the curve concave upward?…

A: We have to solve given Questions.

Q: 3. Find the volume generated by revolving the ellipse whose equation is a² x-axis. 4 лab² (Ans. 3 )…

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Q: y = (11x² + 5)³

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Q: Given the function f(x) = x² + Draw a sketch of the graph of f. 16 - X x>0

A: Follow the procedure given below.

Q: 3) Cindy will require $18,000 in 7 years to return to college to get an MBA degree. How much money…

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Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: Q2-Solve the differential equation dy = - y xcos² (-) dx

A: I am attaching image so that you understand each and every step.

Q: 3) Let r1(t) = and_r2(t) = be two skew lines. Find the equation of the plane which lies exactly…

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Q: 6. Solve dy/dx = 3x^2 - sin y/ x cos y a. -x sin y = x^3 + c b. x sin y = - x^3 + c c. x sin y =…

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Q: A 13.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the…

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Q: Solve the given differential equation by separation of variables. dy = e5x + 4y dx -4e5x 5 + C X

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Q: 1. In x x² dx

A: The given integral is: I=∫16lnxx2dx   So, we can also write as; ∫16lnxx2dx=∫16lnx·1x2dx=∫16lnx·x-2dx…

Q: If the Wronskian W of f and g is t²e5t, and if f(t) = t, find g(t). NOTE: Use c as an arbitrary…

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Q: 3) lim(x - 1)-¹ Inx x-1

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Q: The figure shows the first three in a sequence of squares. The first square in the sequence has a…

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Q: dy 4. Solve the initial value problem : (1+x²). -= yx, y(1) = 2 dx

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Q: Q2-Solve the differential equation dy = y - xcos² (2 dx x

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Q: O cos y (cos x + 1)

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Q: Find the equation of the line tangent to the graph of f(x) = 3 - 2x at x = 3. Provide your answer…

A: The slope of tangent on a curve f(x) at x = a is given by,  m = f'(a)  The equation of tangent on a…

Q: Find a differential equation whose general solution is 7t y = c₁e²t + c₂e-5t = 0

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Q: d²y dy 2. +4 + 4y = 0, when x = 0, y = 1, y' = -1 dx² dx

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Q: Repeated Irreducible Quadratic Factors: Examples Sa++²2a²+1 da

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Q: termine the angle between 0 and 2π that is coterminal with 4 11 5m 3m 그믐

A: Given query is to find coterminal angle.

Q: Ol: a: Graph the function: |y| + |x| = 1

A: Given problem:- Graph the function |y|+|x|=1

Q: Differentiate: 3. y = log₂ (x¹ - x)

A: y = log9(x4 -x) here logerithmic function is given  dlogax/dx = 1/x(lna) use this formula and chain…

Q: 2. ₂(x³ - 3x + 1)dx

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Q: Given the function g(x, y, z) = x²y - 4zex+y, find the slope at P(1,0,1) in the direction of the…

A: Here is the solution