Solve the initial value problem y¹5 = 0 fy= (y(1) = 6 1+x x y¹4 x > 0

Q: 5. Use the limit definition of derivatives to compute f'(x), where f(x) that a, b, c are constants.…

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Q: Jo Sta csc4 x cot6 x dx tan ³ x dx I se sec4 x dx

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Q: find an inner and outer such that y=f(g(x)) then calculate dy/dx  y=tan5x^2

A: Given y = tan(5x²)

Q: Let the matrices and Find each of the following: Ay = and Bx = -4 27 A-441 -4 5 = 2t - [24] X = and…

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A: The given function is

Q: 26. Find a vector perpendicular to both a = [1, 2, 3] and 5 = [3, 2, -1].

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Q: 2. Sketch the graph of the piecewise defined function x² for x 0 Evaluate f(5), f(0), f (-3). g(x)…

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Q: If ƒ(x) = 2x² − 4x + 6, find ƒ'(−2). −12x - 2 incomplete. X syntax Use this to find the equation of…

A: Rule of derivative.

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A: Transformation function h=Horizontal shift k=vertical shifta=scaling factor

Q: The curves F₁(t) = (2t, t5, 4t¹) and 72(t) = (sin(5t), sin(t), t) intersect at the origin.

A: The curves r→1(t)=⟨2t,t5,4t4⟩ and r→2(t)=⟨sin⁡(5t),sin⁡(t),t⟩ intersect at the origin.

Q: Sketch the graphs of the functions f and g. f(x) = 9 - x², g(x) = 2x + 3 -10 y 10 5 A -5 5 -5 -10- X…

A: we have,   f(x) = 9-x2   g(x) = 2x + 3

Q: 3. Suppose a stone is thrown vertically upward from a height of 96 ft above the ground in a vacuum…

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Q: 2. Let C be the parametric curve

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Q: 3. Show that f (x) =x- cos x has at least one zero. Justify your answer.

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Find the work required to pump all the water out of a cylinder that has a circular base of radius 5…

A: Given:A cylinder with circular base of radius 5 feet and height 200 feet where density of water is…

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Q: Solve the given differential equation for x € (-∞, -1) U (1, +∞) 1- y² 1 x² y' =

A: The given differential equation is

Q: 1 Let F(t) = (vt - 4, 4e², ²3). t-3 12 [1² F(t)dt = { Evaluate the definite integral.

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Q: if f'(x) = 5 - (8/x^2) , x≠0, find the value of f(4) given that 2f(1) = 4 + f(2)

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Q: Two measurements are given. Find the absolute difference and then find the relative difference as a…

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Q: Find u. v, uu, ||u||², (u · v)v, and u. (2v). u = 5i + j - 9k, v=i-4j + 5k (a) -44 (b) 107 (c) 107…

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Q: Two friends Korin and Lorie are running a marathon along a straight road. Assume that their…

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Q: Use the information to find and compare Ay and dy. (Round your answers to four decimal places.…

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Q: ) y = -3 ln x + 3x

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Q: A differentiable function f has one critical number at x = 8. Identify the relative extrema of f at…

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Q: Given the vector-valued functions е u(t)= e ti+e-4 + 4tk v(t) = −ti + 4t²j + 4k d find (ū(t) · v(t))…

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Q: Find f', given f(x) = x sin5 (x4) √x+1

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Q: (d) lim x→0 cos(a + x) cos(a — x) * (e) lim x48 * (f) lim xxx 2x - 1 2x + 1 X x In(e³ + 3) In(e5x +…

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal…

A: A horizontal tangent to a curve of a function f(x) at peaks of the function.

Q: Consider the following graph of f(z). 10 -9 -6 a m co 8 6- + 2- b N T -6 -m 3 -60 9 a For 12 X

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Q: Suppose h(x) = f(g(x)). Given the table of values below, determine h' (2). x f(x) g(x) ƒ'(x) g'(x) 2…

A: Solution-h(x)=f(g(x))we have to find the value of h'(2),The chain rule states…

Q: SOLVE: Y" - Sy=0 -

A: given differential equation

Q: Analyze the function below. Which of the following is/are true? 8 f (d) 818 88 x+5 as x→ 1+, f (x)…

A: The function is

Q: 2) Given the function below, determine the intervals on which the function appears to be increasing,…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Use natural logarithms to solve the equation. -0.319t=2 e The solution is t= (Simplify your answer.…

A: Consider the equation

Q: Stan ³ x sec x dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the value of constant c such that the function f is continuous on (-∞, ∞). C = Number f(x) = cx…

A: To find the value of constant  such that the function  is continuous on .

Q: Find each limit, if it exists. (If an answer does not exist, enter DNE.) x8+2 x→∞ x9-9 (a) lim x8+2…

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Q: 10) Given the functions f(x) = 4x² - 5 and g(x)= 15-3x, find (fog)(4). 4 (15-3X2-5 Inverse:…

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Q: Let r(t) = (-5t³ – 1, t² + 5t³, 3t²). Find the line (L) tangent to (t) at the point (39, -36, 12)

A: r→(t)=⟨−5t3−1,t2+5t3,3t2⟩Find the line (L) tangent to r→(t) at the point (39,−36,12)

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Q: Indicate whether the statement is true or false. 9. A normal vector to a line is perpendicular to…

A: As per the Bartleby guide line we only do first part of multiply questions. Please repost other…

Q: Consider the following graph of the function f(x). 10 (b) lim f(x)= x→2¯ (c) lim f(x) = x+2+ y (d)…

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Q: NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to…

A: Consider the set S

Q: 2. Find ƒ' (a) using f(x) = 3x² - 4x + 2. three-step rule if

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Q: The Ninth Gate You arrive at the final gate, which leads into a building-like structure. You hope…

A: The given functions are

Q: 3. Suppose a stone is thrown vertically upward from a height of 96 ft above the ground in a vacuum…

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Q: Find 7' (t), given r(t) = (cos(—2t), sin(−t), −2e¹¹). r' (t) =

A: we have to find the derivative.

Q: Find 7' (t), given r(t) = (sin(t – 1), te-t, 5t ln(5t)). r¹(t) =

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