Given and f'(-1) = Find f'(x) = -5 and f(-1) = 0. = and find f(1) = = f"(x) = 5x + 1

Q: 14. Give a geometric explanation of why 2π/n 1-2 0 r² do = лr² 2 for any positive real number r and…

A: n2∫02πnr2dθ=πr2 For any positive real number r and any positive integer n. Prove this geometrically.…

Q: Use Descartes' Rule of Signs to determine the number of positive real zeros of the following…

A: By using Descartes' Rule of Signs to determine the number of positive real  zeros of the following…

Q: 7. Evaluate: 100 Σ i=60 8. Convert i n logs i=1 into an expression involving sigma notation and find…

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Q: Suppose f(x) is a continuous function where f(9) = 10, f'(9) = -7, and f'(9) = -2. For a final…

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Q: Let s(t) = 6t³ +81t² + 360t be the equation of motion for a particle. Find a function for the…

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Q: sin COS tan 19 19п 19п 4 = = = 18. Пур

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Q: dy Use the Fundamental Theorem of Calculus to find where dx dy dx || cos (1x) ⁹ + sin x 1x…

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Q: A company produces very unusual CD's for which the variable cost is $13 per CD and the fixed costs…

A: The Profit Margin f is defined as:  f(x)= [P(x)/R(x)]×100 Where P(x)= Profit function and R(x)=…

Q: Verify Green's Theorem by evaluating both integrals [ 1² dx + x² dy = [₁ ] (aN_AM) da dA əx ду for…

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Q: Find two positive numbers a and b such that 2a + 3b = 1 and so that a3 + b2 is as small as possible.

A: Find  two positive numbers a and b such that 2a + 3b =1 and so that a3  + b2  is a small as…

Q: Find y'= dy using implicit differentiation: dx a) 2x² - 5y² - xy = 2 dy = b) 3 + 4 = 4 X Y

A: a) 2x2-5y2-xy=2 b) 3x+4y=4

Q: Having taught his algebra students to solve linear-quadratic systems of equations graphically, Mr.…

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Q: The cost, in dollars, to produce a designer dog leashes is C(x) = 4x + 7, and the price-demand…

A: Since, you have posted multiple questions, as per guidelines we are supposed to answer only first…

Q: Find the indefinite integral. (Use C for the constant of integration.) x² + 5 - 5x+/-In(x² +51)+c C…

A: Consider

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Q: 3 Find the equation of the vertical asymptote(s) of the function ƒ(x)=**+2 85°F Partly sunny X=0…

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Q: Ga Time (h) Text messages 0 25 65 Cost ($) 0 5 13 3. Andy's text plan for his cellphone is shown in…

A: (a) to draw a graph. (b) slope, m = ? & what does it mean?

Q: dt 2wt=t²2w³ dw

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Q: Let F(x) = ² 16e4.x-38e³-14e dt. Find an equation of the tangent line to the curve y = F(x) at the…

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Q: Find exactly the vector oppositely directed to v = (3) and half the length of v. < Dell IH

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Q: a. Use implicit differentiation to find the derivative b. Find the slope of the curve at the given…

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Q: Consider the function f(x) Let F(x) be the antiderivative Then F(2) = 5 4 x4 x6 of f(x) with F(1) =

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Q: d²y and find the slope and concavity (if possible) at the given value of the parameter. (If an…

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Q: Find y' and dy a) y = 7 sin (x² + 3x-3) y'= c) 7 y ² - 3x² = 4 dy dx = b) 2 y = X²³-4x+2 y' = De²y =…

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Q: Using only limits of Riemann sums, compute L'₁ (2². 2 (x² – 3x) dx.

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Q: Suppose that a particle moves along a straight line with acceleration defined by a(t) = t – 5/2 in…

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Q: 5. Describe the pattern that is found by taking successive derivatives of the function f(x) =…

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Q: 6. Let f(x) be the function given to the right. Calculate each of the following integrals. (a) f(x)…

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Q: 32 Determine the maximum and minimum values of the function f(x) = 2x+² on the interval -2≤x≤8.

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Q: 13. Find the area of the region bounded by the Parabola y = 3x², the tangent line to the parabola at…

A: The equation of parabola is:y=3x2

Q: A population of squirrels in a forest is observed to be 190 squirrels at time t = 0. After a month,…

A: We have to find P(t) and predict the population size after 2 years.

Q: Scot 2x dx

A: ∫cot2xdx

Q: he limit. (If the limit is infinite, ent (√49 lim t →∞ 49t² + 8 - 7t)

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Q: A particle moves with a velocity of v(t) ft/s along an s-axis. Find the displacement and the…

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Q: Find the arc length L of the graph of r(t). r(t) = 9 cos(t)i +9 sin(t)j + tk, 0≤t≤ 2π

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Q: Evaluate [₁x (x + y)ds where C is the straight-line segment x = t, y = (2-t), z = 0 from (0,2,0) to…

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Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: fx=xx+2,  a=1  &amp;  f1.3 a). Differentiating with respect to x, we get…

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Q: a. Use implicit differentiation to find the derivative b. Find the slope of the curve at the given…

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Q: A product is introduced into the market. Suppose a product's sales quantity per month q(t) is a…

A: The equation of sales quantity is, q(t)=1000t-100t2.   The equation of price of the product,…

Q: = 0.4x + 27. The price- For a small farm, the cost in dollars to produce a containers of ice cream…

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Q: The Taylor series for f(x) = e² at a = 1 is Σn (x - 1)″ n=0 Find the first few coefficients. со 5 C3

A: The Taylor series for fx at a=1 is ∑n=0∞cnx-1n

Q: For the given function, determine the following if possible. If it is not possible, explai You must…

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Q: Determine the dual problem. Solve either the original problem or its dual by the simplex method, and…

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Q: Find f. f(x) = f'(x) = 24x² + 2x +4, f(1) =1, f(1) = −4

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Q: The cost, in dollars, to produce a designer dog leashes is C(x) = 4x + 7, and the price-demand…

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Q: For these problems, use this formula for compounding interest continuously. Round answer to 2…

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Q: Suppose a product's revenue function is given by R(q) = −8q² + 200q. Find an expression for the…

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