dy Find in each of the following: (be sure to use proper notation and simplify) dx (a) (b) y = sin¹ (3x³ + 6) y=e8x (9x² + 3)²

Q: 6. Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

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Q: c) 2x²8x + 4x³ - 4

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Q: 5. (y4 - 2xy) dx + 3x² dy = 0; when x = 2, y = 1.

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Q: A.Given the following functions, find the general solution, the value of the arbitrary constant…

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Q: dx b) √ COS √x cos(1-√√x) 818

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Q: Find the limit of s(n) as n → ∞. [n(n + 1)] 2 s(n) 1 [n(n n²

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Q: Z = (a) What is the equation of the plane passing through the points (2, 0, 0), (0, 2, 0), and (0,…

A: We have to find the equation of plane passes through the points and volume

Q: d) f(a)= (2a-1)² 2a + 5a

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Consider the curve r(t) = (5t² − 3)i + (3t - sin(t))j. - y -5 5 a(t) = -5 5 10 15 20 (a) Find the…

A: The given curve rt=5t2-3i+3t-sintj use the derivative formulas, ddttn=ntn-1ddtsin t=cos tddtcos…

Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

Q: Find the unit tangent vector T(t) for r(t) = 4ti + 7t²j + 3tk. T(t) =

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Q: Can this also be solved using the mean value theorem? Thanks!

A: Given.

Q: 4. [2 marks]. Solve the following system of equations using the Gauss-Jordan elimination method: -2x…

A: If you don't understand any step please comment.

Q: 5 Find the derivative of f(x) = -4√x + T8 Type your answer without fractional or negative exponents.…

A: To find the derivative of the given function.

Q: Find the distance from the point A to the line through points B and C. Then show that the triangle…

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Q: The function f(x) = 2x³ - 39x² + 216x 3 has two critical numbers. The smaller one is x = and the…

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Q: Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t)…

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Q: A piece of cardboard measuring 8 inches by 10 inches is formed into an open-top box by cutting…

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Q: 3. Given the vectors a, b, and c, show how to construct the following vectors using the triangle law…

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Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Given graph of g' is shown below

Q: Use Taylor series you already know to find the Taylor series generated by f(x) = x sin(6x) at x = 0

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Q: so xe x dx

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Q: Use the geometric series f(x) = f(5x) = 1 1-5x ∞ Which of the following is the power series…

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Q: 7. Find the equation of a normal to y = x³ - 3x²+x-1 at x = 3

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Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

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Q: = Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: uppose a company's profits are given by P = x2y, where x is the amount of money they spend on TV…

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Q: EQUATIONS 5y" - (y')4 = y³ sin x yy" + 2x = tan x )' - - 8² 8f + (9) St² - 8³ M dy³ dy² xt' + (t")3…

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Q: 1 4. f₁² (1-x²) dx 5 2

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Q: Find Ž k=0 the convergence Set for each

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Q: Please correct me if i'm wrong. The points where f(x) appears to concave downward appears to be…

A: Given , the point where f(x) appears to be concave downward appears to be (-2 , 2.9 )

Q: 1. a) Copy the graph. YA 4 2 4-20 2 f(x) AR 2 4 x (g(x) b) Use the superposition principle to…

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Q: 1. sin x sin 2x + cos x cos 2x = COS X

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Q: 13. Given f(x) = 2x² − 5x + 14 and g(x)= x − 3 a) Evaluate g(12) b) Determine & simplify f(-2c) c)…

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Q: Which of the following is a linear differential equation? O da-t{1+t²) sec² ædt = 0 O…

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Q: h. Use the second derivative to identify intervals where f(x) is concave up. (-0,3) X i. Use the…

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Q: Evaluate ſ F . n dS if F = (x + y² ™)ī − (2x)j + (2yz)k and $ is the surface of the plane 2x + y +…

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Q: 2.4 Write functions of the following graphs. 2.4.1 2.4.2 + -3 -2 -3 N 0 -1+ 34 2+ 0 - 2

A: Above question is solved

Q: (y¹ - 2xy)dx + 3x² dy = 0

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Q: Use cylindrical coordinates to calculate: Sw(x² + y²) dV = [[[_x² + y²³ av W: x² + y² ≤64, 0≤ z ≤ 16

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Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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Q: Consider the function f(x) = x² + 2x - 8 x - 3 a. Find the first derivative. f'(x) b. List any…

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Q: Find the value of C so that y(t) = Ce2t satisfies the initial condition y(1)=1

A: Substitute t=1

Q: 2 √9x²-16 x² dx

A: We will use substitute method to solve the integration

Q: Let f(x) = x¹ - 50x² 3 (a) Use the definition of a derivative or the derivative rules to find ƒ'(x)…

A: "since you have posted a question with multiple subparts,we will solve first three subparts for…

Q: The graph below is the function f(x) Find lim Find lim I→-1- Find lim 4 3 I→-1+ in 2 01 I-1 es 1 2…

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Q: Find the the e following: sinx first maclaurin four Series nonzero for terms of each (21) S² Tara d…

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Q: (b) If f(x)= |x-1| is now restricted to the domain x ≥1, find f¹(x) and state its domain and range.

A: Given problem:- If fx=x-1 is now restricted to domain x≥1, find f-1x and state its domain and range

Q: (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) = PY PW POY

A: A particle moves according to the position function st=e4tsin5t To find the velocity and…

Q: (iv). limit x-0 ²-1 - x - x ²³/₂2 - x² - x ²%/ e 6 x4

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