For y = ln(x7 + 3x - 9), to find y' would require the chain rule. If y = f(g(x)), find an f(x) and g(x) that would allow you to use the chain rule.

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Q: Find the quotient and remainder using long division. x6 − x4 + x2 − 1 x2 − 1

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Q: Let f(z) —7cosz —6tanz f'(x) = f' 4TT 3 J

A: f(x)=7cos(x)-6tan(x)

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Q: 8. Find the equation of the line that passes through points C(-2. 1) and D(2, -3).

A: eouation of line passes through two points (x1, y1) and ( x2,y2) is given by  y - y1 =y2 -y1x2-x1(x…

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Q: $ 1 b) y = √√x lad

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A: The diameter of the hemisphere is 45 meters. The volume of the hemisphere = V(r)=23πr3

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A: We have to find out limit

Q: Solve the following DE: (1+ y² + xy²) dx + (x²y + y + 2xy) dy=0 O 2x+y²(1+x)² = C O 2y² + x²(1+x)²=c…

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Q: 227. y' = 3x + xy

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Q: 4. Convert the following integrals to polar coordinates. Then evaluate them. 1-x² A. 0 LIVE -1…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: (1, √3) (a, b) = (-2, (-2,√3) (2√3, 2) (√3, 1) (√3, -1) - (a, b) - (a, b) = - (a, b) = (-1, √3) (a,…

A: Given query is to find the Cartesian coordinates of the point P.

Q: Evaluate the iterated integral 3π 32 SS 2π x cos y dy dx.

A: Given, ∫23∫π3π2x cos y dy dx

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A: At 10:17 A.M. you pass a police car at 55 mph that is stopped on the freeway. You pass a second…

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A: See the details solution in below

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Q: Problem 2: Given the differential equation (yetanx sec² x - 1) dx + etanx dy = 0: a. Identify…

A: The objective is to solve the above question.

Q: 6. Consider the function f(x) with f(x)dx = 5 and Jo (a) Evaluate [² 2f(x) dx (b) Evaluate ff(2t)dt…

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Q: Q.1. Which of the following function is even ? 4 _A) f₁(x) = x² + x³ -B) £₂ (X) = x² + x² + x³ c) £3…

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A: Find the derivative of cross product of vector r and its derivative.

Q: find ab if |al=5 161=7 and the angle between a and 6 is 1/9 radians 9₁6=1

A: Given query is to find the value of a.b

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A: let v be the volume then given dvdt=65cm3seclet side of square base = a height = h volume ( v)…

Q: Given the function below ✓50x³ + 75 Find the equation of the tangent line to the graph of the…

A: Given, f(x)=50x3+753

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Q: A population P exhibits logistic growth according to the model +=0.05(1-when -=0.05P 1- where the…

A: Concept: The explicit solution for the population at time t is P(t)=751-Xe-0.05t Now at t=0 the…

Q: 19. If z = f(x,y) has continous partial derivatives, x = s + 2t and y = s - - 2t, show that 2 2 2(0)…

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Q: Differentiate: x¹0 cos(x)

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Q: Find the differential of the function. y=x² - 8x + 2 dy = Evaluate it at the given values of x and…

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Q: 16. f(x) = x² - 2x³; [-2,2]

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Q: Use the tables for f(x) and g(x) to evaluate the expressions below. Write your answer as an integer…

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Q: Given the differential equation (ysinx-cos²x) dx + cos x dy = 0 a. Determine if the differential…

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Q: 5. Determine the equation of the tangent to f(x)=2x-2 where x = 3

A: The given function is  f(x)= 2x-1x-2 Find the equation of tangent line at x=3.

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Q: Determine the domain i. R (t) = √√t²-9, In It-31, t² + 2+ + 8) 11 R (t) of the following functions…

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Q: Find the PS of dy dx ex sin y + e cos x ex cos y + ey sin x y(0) = π/2

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Q: 12 1.²³² 2. Consider a) Estimate this integral by using 4 rectangles with r 1 x+1 -da

A: a. right end points

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Q: 2. Form a polynomial f(x) of least degree having real coefficients, i as a simple root, 0 as a root…

A: We have to form a polynomial f(x) of least degree having real coefficients, i as a simple root, 0 as…

Q: 3. If |ā|=12, |5|=8, and the angle between them is 60°, determine the magnitude and direction of…

A: See the details solution in below

Q: Find a polar representation for the curve whose Cartesian equation is x² + (y + 1)² = 1. 1. r = 2. r…

A: The equation of the curve in cartesian coordinates is given by x2+y+12 = 1 Relation between…