Find the derivative of the following functions. Whenever possible, express answer in factored form. 2. y = (3x¹-2x²+4) 2

Q: Given the function () below, decompose A(z) into component functions f(x) and g(x) so that A(z) —…

A: We can answer both the question in the below steps.

Q: For the given graph of the function f, -4 -2 4 2 -2 -4 2 on the left, 4

A: In inverse function the value of x and y interchange. and it is reflected about y = x a.

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Q: Solve the equation (r + sinx - cosx) dr + r(sinx + cosx) dx = 0 Hint: Exact O r^2 - r (sinx - cosx)…

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Q: 3. lim_ log₂ (x) x-15 4. lim (cos(x)-1)

A: answer 3 and 4 only Given :3.limx→15log2x4.limx→0cosx-1x

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Q: Eliminate A and B from x = A sin(wt + B). w being a parameter not to be eliminated. Ox"+w^2x = 0…

A: To form the differential equation.

Q: How does the x^4 and the 3x^3 become to 4x^3 + 9x^2. I understand how you got 4x^3 but not the 9x^2.…

A: We know, d/dx (m*xn)=mn(x)n-1 for any real numbers m,n

Q: How much more does Karla earn than Bert? tA $ Package Delivery Driver Salaries Misha $39,731 Charles…

A: Given Data: Package delivery driver salaries Misha $ 39,731 Charles $ 41,189 Bert $ 42,098…

Q: F(x)= x³-2x² 3 2x Manipulate the function algebraically and differentiate without using the quotient…

A: Topic = Derivative

Q: Use a local linear approximation to approximate the value of 6(1.99)2 +3.02 by a rational number.

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Q: Evaluate the integrals 2. 88 1 Ĵ dx 3 x(lnx)³

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Q: Directions: Consider the following function f(x). Part 1 - Difference Quotient If h = 0, then the…

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Q: 1. A balloon is released from the ground 30 feet from an observer. The balloon rises directly upward…

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Q: Find the second partial derivatives of the function f(x, y) = x³y5 +7x4y. 1. 2. 3. 4. 02 f дx2 - 82f…

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Q: f(x) = b-2x 6 x-b if x < -1 if x ≥ -1. Find the two values of b for which f is a continuous function…

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Q: 2x + 3y - 1) dx + (4x +6y + 2) dy = 0 Give the: a. homogeneity b. degree c. reducible…

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Q: In the figure, the equation of the solid parabola is y=x²-6 and the equation of the dashed line is…

A: Given data:- The equation of a solid parabola, y=x2-6  The equation of the dashed line,  y=5x

Q: Consider the function of two variables f(x, y) = ln(5x 6y) + e* cos(3y) (a) Compute the first-order…

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Q: y = x(2x + 1)³, find y".

A: Topic = Derivative

Q: Solve

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Q: Calculate 7 7 8 [x²dx=114 Sx²dx= 2 7 7 7 (6x - 9)² dx, given the following. 7 1 (6x - 9)²dx = 169 3…

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Q: Evaluate the indefinite integral. [x³(x®. x5(x6 + 1)³/² dx

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Q: The graph of f is given. 0 1 X (a) What are the domain and range of f-¹? (domain) (range) (b) What…

A: Here, note that the domain of the given function f(x) is [-3,3] which are the x values for which the…

Q: Find the equation of the tangent plane to the surface determined by at x = 3, y = 4. 2 = x¹y¹ + z =…

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: Solution

Q: Let f(x) = 4√ If g(x) is the graph of f(x) shifted up 2 units and left 4 units, write a formula for…

A: find the equation of g(x)

Q: The graphs of y = f(x) and y = g(x) are shown below. If g(x) = af (b(x − h)) + k determine he values…

A: The graphs of y=fx and y=gx has been shown above.Given that,  gx=afbx-h+k, we need to determine the…

Q: d Let Arctan² (3e) dx ke*Arctan(f(x)) g(x) Compute kf (0) - g (0) - 3

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Q: Solve the ODE d²c dt² dc +4 = -2C dt at C(0)= dc dt = 1

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Q: 4) Show that every plane that is tangent to the surface x² + y² y² = z² contains the origin.

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Q: What is the value of k so that d dx -sin(kx²) = 6xcos(kx²) 2

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Q: Solve the DE (6x + y2) dx + y (2x - 3y) dy = 0. Hint: Exact O 3x^3 + xy^2 - y^3 = c O 3x^2 - xy^2 -…

A: Given differential equation:- 6x+y2dx+y2x-3ydy=0

Q: An object moves along the curve with equation 10+ 3967 S 8 6 5- 4 w to 3 da 2 1 10 -9 -8 -7 -6 -5 -4…

A: Observe the points on the graph for the limits and find the derivative of y with respect to x and…

Q: Q1. Find Domain and Range of у sin(x)

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: If z = (x + y)e", y = 5 - t², find dz/dt using the chain rule. Assume the variables are restricted…

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Q: Find the Laplace inverse of the following: 2 s 3 s²-8 215248 1) 3) 2 s (s+3)²+6

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Q: Directions: Consider the following function f(x). Part 1 - Difference Quotient If h = 0, then the…

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Q: Calculate the definite integral by referring to the figure with the indicated areas. ff(x)dx 0 Area…

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Q: using the definition of Laplace, solve the ff: 1. L [cos at] 2. L [cosh at]

A: We have to use the definition of Laplace transform to solve  (1) L{cos(at)}

Q: Find the third derivative of f(x)=^3sqrt(9x+1)

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Q: -3 -110 lim g(x) = x→2- lim g(x) →2+ = lim g(x) = = x→2

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Q: The graphs of z = 6, y = f(z) (solid) and y=h(z) (dashed) are shown; the graph is not drawn to…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: V = ∫πy2dx here y = 12-x limit from -4 to 12

Q: If z = (x + y)e and x = 7t and y = 1- t², find the following derivative using the chain rule. Enter…

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Q: Directions: Consider the following function f(x). f(x) = 4x² - 3 Part 1 - Difference Quotient If h =…

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Q: 0 -2 ex+1 dx 7- ex+1

A: Given query is to find the value of the integral.

Q: Solve for the unknown/s. 1. A particle moves horizontally according to the laws the laws--12r+1.…

A: Topic:- application of derivatives   Note:- as per our guideline if more than one question uploaded…

Q: Free fall. In dropping a stone or an iron ball, air resistance is practically negligible.…

A: Given     Acceleration of gravity, g=9.80 m/sec2=32 ft/sec2 At t=0, v=y'=0