Find the equation of the tangent line to the function f(x) = −3x³ − 3x² − x + 3 at the point (-1,4). Give your answer in the form y = mx + b.

Q: nd an equation of the tangent plane to the surface at the given point. X+y+z=12, (3,5,4) And find a…

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Q: lim √2³ - 2² sin V DIF KIN

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Q: Identify a function f that has the given characteristics. f(–5) = f(2) = 0;  f '(-1.5) = 0,  f '(x)…

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Q: Consider the following limit. lim (13x + 2) x→2 Find the limit L. (a) Find the largest &> 0 such…

A: The given limit is .The aim is to find the value of  for which .

Q: 3. and (5, 3, -8) are endpoints of a diagonal. Find the coordinates of the remaining six corners.…

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Q: Problem 4: A cylindrical tank contains 500 gallons of water. A plug is pulled from the bottom of the…

A: Using given model, we can solve all the parts.Note : According to our guidelines, we can answer only…

Q: cos(x) lim x → (π/2)+ 1 - sin(x)

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Q: Find the average rate of change for the given function over the indicated values of a. If necessary,…

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Q: 3. tion f(x) that satisnes lim f(x) = 0 8118 lim f(x): =10 x-4- Putting all together: Sketch a graph…

A: The function satisfies the following conditions,The aim is to sketch the graph of the function that…

Q: 4. Zero of more of the following statements are true for all real numbers a, x, and y. For each…

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Q: limt 3 (t¹ – 5t³ + 2) = - If the limit does not exist, write "Does not exist" without punctuation.…

A: To evaluate each of the following limit.

Q: Find y' 2x-3 y= 3x + 1 y"=0

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Q: tion f(x) that satisnes lim f(x) = 0 x118 lim f(x) = -X x→4- Putting all together: Sketch a graph of…

A: The function satisfies the following conditions,The aim is to sketch the graph of the function that…

Q: Find the x-value at which is discontinuous and determine whether is continuous from the right, or…

A: In this question, we will find continuity or discontinuity.

Q: d. e. 8x³10x² - 12x - 15 2x² - 3 I 3x4 - 2x² - 5 3x² - 5 13 X x² − 1⁄2x³ + 3x² −5/2x+12/20 - f. 9 -…

A: Solve given expression using long division method

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: For each value below, enter the number correct to four decimal places. Suppose an arrow is shot…

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Q: Consider the parabola y = 6x - x². (a) Find the slope of the tangent line to the parabola at the…

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Q: y-2 (x - 2)²· Indicate the range of z using interval notation. Note: To answer 'infinity', use 'oo'…

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer…

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Q: Let h(x) = 2x² 9-x²

A: h(x)=−2x29−x2

Q: u = (1,7,-3) and v = (3,-2,3) Find u. v Find u x v Find an equation for the plane through P(4, 1, 1)…

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Q: Evaluate the integral. (Use C for the constant of integration.) [7 (tan²(x) + tan^(x)) dx

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Q: √x³+9y³ 5x +COS (+)

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Q: CWORTMA Problem 2: For each set of polynomials a. p(x) = 5x²-3x+1 TELENO 3x +1_q(x) = x-1 Cecc 1.…

A: A) p(x) = 5x^2 - 3x + 1, q(x) = x - 1Synthetic Division:We want to divide p(x) by q(x), which is x -…

Q: Answer the following problems and show your complete solutions lim u→-1 u²u³+u-1 u³ +1

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Q: Find the derivative of the function: h(x) = 3/x - 2/x3 + 1/x4 h'(x) =

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Q: The slope of the tangent line to f(x) = 3x² − 1 at x = 2 is 12. false true

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Q: Q5: Draw and Find the Position of the Centroid of the Figure bounded by ye with the x-axis and the…

A: Using integration, we can find the coordinates of centroid.

Q: Consider the following. 8 6.³. dt = Let t = 8 tan(0) and determine the following. t = 0-0 = dt 64 +…

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Q: Find the formula for the nth term in the sequence: −3/2 , −1/6, 1/12, 3/20, 5/30, . . . Integers…

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Q: The number of foreign language teacher jobs in the United States for the 2022-2023 school year can…

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Q: n 2013, the average surface temperature of the earth was 58 (degrees Fahrenheit) and, according to…

A: In , the average surface temperature of the earth was Incresing at a rate of Let T denotes the…

Q: 2.(15) The graph af / is given below. Use the graph of / to determine the given limits. Enter ONE if…

A: we can observe as x approach curve approach value -1.

Q: The Taylor expansion of f for x→ 10 is f(x) = 10 + 3(x-10)² + 2(x-10)³ + 0((x a) ft (10) = -12 6) fr…

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Q: II2. Find an equation of the plane that contains the intersection points of the ellipsoid 9x² + 4y²…

A: To find the equation of plane?

Q: f(x) = x² 8 x + 2 x - 6

A: f(x)=x+2x2−x−6

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: f(x) = sin(0), 0 - 10 <0 <0 0 ≤0 ≤ 10 Find lime 5 f(x). If the limit does not exist, write "Does not…

A: Given: To Find .

Q: First find all constant solutions, then solve explicitly: dz da - 2²0³ 0² - 72² d0

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Q: Determine whether the graph of the function has a vertical asymptote or a removable discontinuity at…

A: The function is  .

Q: do #11

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Q: Let g(x) = x² and h(x) = (fog)(x) = sin x². Then f(x) = (gof)(x) = and

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Q: Use first principles to differentiate the function f(x) = √√2x + 1

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Q: Find the average cost per item (the average rate of change) when increasing production from 200…

A: Solution-In the given graph we know when production is 200 units cost is 11000,and when production…

Q: Solve sinx-cos² * = cos² = 1 on the interval 0≤x < 2π. п 4 " бп 4 п 3п 2' 2 0, π Ο 0, π, 2π

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Q: Find the derivative of the function.  s(x) = √x + 5/√x

A: The given function .The aim is to find the derivative of the function.

Q: Find the distance from the poinst (-5, 2, -3) to the z-axis.

A: Given:  Point: ( -5 , 2 , -3)

Q: (a) Find the slope, m, of the tangent to the curve y = 4 + 5x2 - 2x3 at the point where x = a. m=…

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Q: Let f(x) = ²+82 +12 Determine the values of a for which has a vertical asymptote. If multiple such…

A: we have to find the values of vertical asymptotes.