Find the volume of the solid obtained by rotating the region bounded by y = 7x², x = 1, x = 4, and y = 0, about the x-axis.

Q: If tan(0) = -and sin(0) > 0, then find (a) sin(0) = (b) cos(0) = (c) sec(0) = (d) csc (0) = (e) cot…

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Q: Let g(u) = 8u +4 Determine the derivative of g.

A: The given function is,

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A: Given: Let  and To Find:

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A: A particle is moving along the x-axis. The position of the particle at time tis given byTo find the…

Q: Using either the triangle inequality or the reverse triangle inequality, prove the following: ii)…

A: To prove the statement |2x−3|≤5 when |x−3|≤1, using the triangle inequality. The triangle inequality…

Q: Classify the discontinuity in the following function. x²-12x+32 x-4 f (x) = The function has a jump…

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Q: 1 (a) f(x) =====₁ x+1 (b) f(x) = √√√√x − 4 (c) f(x) = 1 x-3 (d) f(x) = 2x² + 3x +9

A: To find the domain of each of the following functions.

Q: Consider the helix r(t) = (cos(3t), sin (3t), - 2t). Compute, at t = : A. The unit tangent vector T…

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Q: (It cosx) y when X = sin x (sinx + sin x cos x - y) ¹|2 y = e 2

A: The given differential equation is

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A: Vertices (0,2) and (6,2)Asymptotes y=2x/3 and y=4- 2x/3Find the equation of hyperbola.

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Q: 5. Answer the following questions. (b) (c) Find the direction vector of the line given by parametric…

A: The given  equation of line is

Q: Evaluate the indefinite integral Ss sin³ v cos¹vdv = + C

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral St 15…

A: We have given,Limit : 1 to 15function: ln(x) / (3+x)n = 8

Q: The path of a diver is modeled by f(x) = − 4 x² + 24x + 9 + 13 where f(x) is the height (in feet)…

A: Given,

Q: 1. State the definition of Continuity in relation to limits. 2. Write the definition of a derivative…

A: (a) State the definition of continuity in relation of limits (b) The definition of derivative…

Q: Find the first, second, and third derivative of the following function. h(x) − (−8x − 4)" a. h'(a) T…

A: Given,

Q: If f(x) = Σ22" and g(x)= n=0 n=0 n=0 na", find the power series of f(x)g(x).

A: Givne series

Q: The graph of f' (not f) is given below. At which of the marked values of x is A. f(x) greatest x =…

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Q: A solid ball is thrown straight upward from the ground y0 = 0 feet with initial velocity v0 =…

A: A solid ball is thrown straight upward from the ground y0 = 0 feet with initial velocity v0 =…

Q: Define each integral Stan² tan²0 de S₁4,da (24/3 +524+n)dz

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Q: (2xy + x² + x4) dx − (1 + x²) dy = 0

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Q: 3. Let a=⟨4,5⟩ and b=⟨3,−4⟩. Show that there are scalars s and t so that ?a+?b=⟨−10,−28⟩

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

Q: Let f(x) = x+1 Write your answer completely simplified and in factored form. f'(x) =

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Q: O The following differential equation is a Euler equation. Find the general solution of 2x²y" + 5xy'…

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Q: We are given f(x) = 3x2 and f '(x) = 6x. (a) Find the instantaneous rate of change of f(x) at x=4.…

A: Given, f(x)=

Q: Find the indefinite integral. (Use C for the constant of integration.) 13 12 dx 1+ 4x²

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Q: • We can use 1 or 2 triangles to find the [Select] • We can use antidifferentiation to find the…

A: I  am going to solve the given problem by using some simple calculus to get the required result of…

Q: Consider the function y = 2e4. Which of the following statements is true for y? O y'=y Oy = /v O…

A: given,

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Q: Let P be the plane containing the point (-11, -2, 1) which is parallel to the plane z + 3y + 4z= -3…

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Q: Consider the function f(x) = 8 3x - 1 - (a) Compute the derivative f'(x) of f(x) using the limit…

A: given

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Q: Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x.…

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Q: A. Evaluate the following limits: 3x²-2x-8 x-2 ii. lim 4x²-3x² +5x-2 i lim 4x²+x-7 5x² +7x+1 i lima

A: Since you have posted multiple question, which are not interlinked so i have solved the first…

Q: The diameter of a sphere is measured as 80 ± 1 cm and the volume is calculated from this…

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A: Domain is the value of x for which the function is defined. Domain of the function is : (-2,7) Range…

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Q: Consider the functions z = ex In y, x= In (u cos v), and y= u sin v. dz əz (a) Express ди (b)…

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Q: Let f(x) = 2x - 1 3x + 2 a. Find the domain of the function. b. Find the y-intercepts, if any. c.…

A: By the answering guidelines of Bartleby, we can answer only first three subparts, plesase post other…

Q: 15. Write an equation for a function whose graph fits the description given below. The graph of f(x)…

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Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 3. y' = x - 2y Ans.…

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Q: f(z) 2+3x1x², find f'(5).

A: f(x)=2+3x−4x2, find f′(5).

Q: for g(x) = ln(1-x^2) and f(x) = sqrt(x + 3), determine the subset of the domain of g on which the…

A: To determine the subset of the domain of g(x)=ln(1−x^2) on which the composition f∘g is…

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.4 cm. Use…

A: The solution of above question is written below.side of cube=30cmpossible error in measurement…

Q: 5. Use the table of ordered pairs to determine the value of each composite function. f(x)=x²-15 g(x)…

A: f(x)=x2−15g(x)=xxf(x)xg(x)1−14112−11423−69341164510255621366734497

Q: A function f is said to have a removable discontinuity at a if: 1. f is either not defined or not…

A: The given function is; f(x)=(2x2+3x-14) /(x-2)

Q: Use implicit differentiation to find the derivative of y, where y is a function of x defined by the…

A: 3x2+9xy2=5x3