If f(x) = 3+3x - 3x², find f'(-5).

Q: Solve the following differential equation dy dx 1 1+x8 = 4. 3y X such that y(1) = 0.

A: Given Linear differential Equation is given as follows standard form of linear equation

Q: Find the derivative of the dot product (u(t) • v(t)) if u(t) and v(t) equal the following (see image…

A: Given vectors are we are to find the derivative of u(t).v(t)

Q: 3. y = −x² + 3x + 1, y = -x + l

A: Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: Part 3: Explain a. Differentiate the following function(s) using the chain rule. b. Then,…

A: Chain rule:

Q: The graph below is the function f(x) -5-4-3-2 4 3 2 4 -2 2 3 4 a Determine which one of the…

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Q: In Exercises 55-62, find the derivative of y with respect to x, 1, or 0, as appropriate. 55. y = In…

A: ** As per our guidelines, we are supposed to answer only one question at a time. Since you have…

Q: 4. Suppose A, B, and C are the vertices of a triangle. Evaluate AB + BC + CA. Write a sentence…

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Q: Determine whether the given function is continuous. You can verify your conclusions by graphing the…

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Q: Consider the following. و + شہری ۔ شہر = (f(x (a) Find F(x) and f(x). f(x) = F(x) = (b) Graph Rx),…

A: Given:To find:f'(x) and f''(x) and monotone intervals

Q: The length of a 12- foot by 8-foot rectangle is increasing at a rate of 3 feet per second and the…

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Q: 5. The shape shown below is made up of 8 equilateral triangles. Let TQ = u and SQ = v. T ū Write an…

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Q: 2. The graph of fbelow consists of four line segments below. Let g(x) = f*₁ f(t)dt. -3 -2 -1 0 -1-…

A: Fundamental Theorem Calculus :-If a function f(x) is continuous over  and differentiable over  and…

Q: - Use the graph of f to determine the value of limx→4 f(x). lim f(x) = x→4 y = f(x) -4 T -3 -2 -1 8-…

A: given graph of function to find the limit.

Q: Convert 3.748° to degree-minute-second form. If necessary, round your answer to the nearest second.…

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Q: Given point S(0, 1, 1) and 4y+3z=-12, find the distance from the point to the plane.

A: To find the distance of the point (0,1,1) from the plane 4y+3z=-12.

Q: The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest…

A: Given that, the Carbondale Hospital is considering the purchase of a new ambulance. The decision…

Q: BETTER UNDERSTANDING. 1. If y'=0 at (a,b); then a) (a,b) is either a maximum or minimum point b) no…

A: 1.] If y' = 0 at (a,b) That means there are stationary points between (a,b) throughout which…

Q: Answer the following. Round your answers to the nearest hundredth. 8π (a) Convert - radians to…

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Q: - Find 3- y = dx for the following x² (1-2x)³ (3x+1)¹/3

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Q: Determine whether the function is continuous at the given point c. If the function is not…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: For f(x)=x², the instantaneous rate of change is known to be -4 at x = -2. Find the equation of the…

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Q: 3. Determine whether the given vectors are orthogonal, parallel, or neither. (a) a =, 6= (b) a =, 6=…

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Q: Question 1 Sketch the graph of f(x); do not forget to keep some sense of a scale and to identify any…

A: The given function is

Q: For y = f(x), we define the [Select] of f at x, denoted f'(x), by f(x+h)- f(x) h if the limit…

A: For function y=f(x), they have been defined f'(x) of f at x, and it is called derivative in…

Q: Find the arclength of y = 3x³/2 on 2 ≤ x ≤ 3

A: Arclength of a curve.

Q: Find the average rate of change of the given function between the following pairs of x-values.…

A: As per our guidelines, we are supposed to answer only one question with a maximum of three subparts.…

Q: The price of a product in a competitive market is $400. If the cost per unit of producing the…

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Q: Consider the differential equation (4xy² + 3y + Ax²y) + (4x²y + Bx + 2x³) dx = 0 (a) Find the values…

A: Given differential equation:-To find the values of and that make the differential equation exact, we…

Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 100e−x2 − 5y2 − 7z2 where T is…

A: T(x,y,z)=100 e-x2-5yz-7z2 is the given equation and we have to findrate of change of temperature…

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: By using properties and algebraic methods to find the following limit., where

Q: Find the equation of the tangent line when x=4 for the curve y+- = 3

A: y+xy=3 at x=4y+4y=3y2+2=3yy2−3y+2=0(y−2)(y−1)=0y=1,2(x,y0)=(4,1),(4,2)

Q: Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved…

A: Given that the region R is bounded by the curves in the first quadrant.

Q: Suppose the winner of a $15,000,000 sweepstakes will be paid $500,000 per year for 30 years,…

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Q: lim (√x³ – 5x² – x) _ x →∞

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Q: Find the slope of the tangent line to the graph of (x, y) =(sin(t), t²) when t = 2 slope= dy dx

A: (x,y)=(sin⁡(t),t2) when t=2

Q: Given y=-2f(2-3x)+1 , solve for x

A: Given equation:

Q: Find the average rate of change of the given function between the following pairs of x-values.…

A: Average rate of change of f(x) over [a,b] is given by

Q: What is the tangent unit vector for u(t) if u(t) is equal to the following

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Q: 26. Which of the following planes are identical, which are parallel to each other, and which are…

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Q: 4 cos(t)-4 Use scratch paper to fill the table below, and guess the value of lim₁→ h(t), where h(t)…

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Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 34 cm to a length…

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Q: Calculate the steady-state current LRC. series Circuit with the of an specifications: L = 1(h) R =…

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Q: f(x): -x+4, -x+3, -3, f(-6) = lim f(x) = lim_ f(x)= 2+6+ lim f(x) x < -6 -6 ≤x≤4 f(4) = lim f(x)=…

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Q: Use the graph of f(x) above to estimate the value of f'(0) to one decimal place. f'(0)=

A: To estimate f'(0)

Q: What are the zeros of the polynomial f (x) = 4x(x − 2)² (x + 7)? Check all that apply. U n n U x = 7…

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Q: An oil storage tank ruptures at time t= 0 and oil leaks from the tank at a rate of r(t)= 80e-0.01t…

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Q: 26 13. Find the limits: a. lim 1+ x-+∞ 3 X X Axess M18 ANO

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Q: 2. If f(w, x, y) = (6w+1) cos(3x²+ 4xy³ + y), find the partial derivatives fw, fx, and fy.

A: Partial differentiation

Q: 26. Let E be the set of all even integers, and let O be the set of all odd integers. Let X = = {n =…

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