Find f'(t) if f(t)= -2t² - 8t+7. f'(t) =

Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to write the given function as a composition of two functions.

Q: Let an = 1 for n = 1, 2, 3, ... . Write out the the first three terms of the following sequences. 3n…

A: Given  To find (a)  then find (b)  then find (c)  then find (d)  then find

Q: Math 152 metric IHU 3. In this problem we'll evaluate the integral cos²(z) sin³ (2) dr. (a) First,…

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Q: Find the square root of 7225 with the modern method

A: A number's square root is a value that, when multiplied by itself, returns the original number.

Q: Consider the equation below. f(x) = 4x³ + 9x² - 54x + 1 (a) Find the intervals on which f is…

A: In this question, we will find the interval of increasing and decreasing.

Q: (a) Find and sketch the domain of the function f(x,y)=√x+2+√√√y+3 (b) Evaluate the limit -8xy lim…

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Q: If what does the following integral equal? -15 -50 [9f(x) + 2g(x) - h(x)]dx = -15 |_| f(x)dx = 15…

A: The integrals are given asTo evaluate: The value of

Q: dy d²y Find and dx dx² x = t² + 2, y = t² + 3t dy dx d²y dx² For which values of t is the curve…

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Q: 3 Use algebra to find the point at which the line f(x) T- 4 59 6 h(x)= - Y 4 3 C Write the values of…

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Q: Suppose f(x, y) = (x - y) (25 - xy). Answer the following. Each answer should be a list of points…

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Q: -4-3-2 VA 3 2 1-2 x = – 1 y = 1 3 4 5 x x = 2

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Q: Sx ³√x²+4 3 S

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. 5 r…

A: r=5θ,π2≤θ≤2π

Q: Find the domain of the function. h(u, v) = √3-u² - v² Ou+v≤3 Ou² + v² 0 Ou+v<3

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Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: The given parametric equations

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) =x² + y² subject to the…

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Q: S Write an equation for a line parallel to y y = -4x + 4 and passing through the point (4,-2

A: To find the equation of a line parallel to y=−4x+4 and passing through the point (4, -21), you can…

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Consider the sequence

Q: Sketch the level curves of the function corresponding to each value of z. f(x, y) = 4x + 6y; z = -2,…

A: Consider the function

Q: TO Find the length of the curve y = In (2 sec x) for 0 ≤x≤ xs 6 The arc length of the curve is (Type…

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Q: Find a formula for the nth term of the sequence where an is calculated directly from the value of n.…

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Q: Write the equation 52 = 25 in logarithmic form.

A: Write the equation  in logarithmic form.

Q: 9. Locate all relative maxima, relative minima, and saddle points of the fol- lowing function f(x,…

A: The given function is

Q: What is the center of the sphere given by the equation x² - · 6x + y² – 2y + z² +82 +17 = 0? -…

A: The standard equation of a sphere is given by  where (h,k,l) is the center of the sphere and r is…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Solve the given initial-value problem. Y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -5, y'(0) = 1

A: y'(0)=1

Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 1;…

A: Form a polynomial f(x) with real coefficients having the given degree and zeros.Degree 5 ; zeros: 1…

Q: Consider the function INTERMEDIATE WORK Using calculus give a sketch of y. Make sure you include the…

A: The given function equation is

Q: Suppose a triangle in space has vertices (a, b₁, ²₁), (a₂, bz, C₂) and (93, b3; (3). Explain how you…

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Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O None of…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: 4. Three large tanks contain brine, as shown in the figure below. pure water 4 gal/min A 300 gal B…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 12 + 2x -…

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Q: J 4³ (u + 1)² du

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Q: Air Traffic Control An airplane flying at an altitude of 6 miles passes directly over a radar…

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Q: To test this series for convergence ∞ n=1 n n6 + 7 You could use the Limit Comparison Test,…

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Q: Calculate the L4 approximation for f(x) = cos² x on TU I 4 2

A: The left Riemann sum∫abf(x)dx≈Δx(f(x0)+f(x1)+f(x2)+⋯+f(xn−2)+f(xn−1))Δx=b−an

Q: An account earns an APR of 4.7% compounded as often as imaginable ("compounded continuously"). The…

A: The given rate is, r=4.7%=0.047 compounded continuously.For the continuous compound, the annual…

Q: For the following differential equation d²y dt² + 4y = 1 cos (21) a. Find the general solution b.…

A: The given differential equation is

Q: Let L denote the left-endpoint sum using n subintervals. Compute the indicated left sum for the…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: The function is given byTo determine: The absolute maximum and minimum values of the function.The…

Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 5x² + y² = 4. maximum value:…

A: To find the maximum and minimum values of f(x,y)=xy on the ellipse 5x^2+y^2=4, you can use the…

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: If what does the following integral equal? 4 19 q(s)ds = [ q(s)ds = 13 and La q(s)ds = 10.7

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Q: Write an equation for a line perpendicular to y y 4-4 and passing through the point (-8,7)

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Q: Find an equation of the tangent line to the curve at each given point. x=2-3 cos 6, y = 3 + 2 sin 8…

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Q: Find aw/as and aw/ât using the appropriate Chain Rule. Values Function w = y³ - 2x²y x = es, y =et S…

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Q: Is the series convergent or divergent? If convergent, is it absolutely convergent? cos (πn) e-n COS…

A: Consider the series