Obtain the following limits: lim (1+ x48 1 lim x-0 3x X 1 sin 3x

Q: (f) (g) Find the absolute maximum and absolute minimum of g(x). On what interval(s) is g(x) concave…

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Q: Find the exact length of the polar curve described by: r = 10e-0 on the interval 9 2 ㅠ T≤ 0 ≤ 9TT.

A: The arc is any part of the Circu mference of the circle. The length of arc can be found by using the…

Q: A particle moves according to the function s(t) = t³ - 3t² - 24t+5. When is the particle slowing…

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Q: At time t=0, a particle is located at the point (1,5,4). It travels in a straight line to the point…

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Q: Find the area A of the region that is bounded between the curve f(x) = −2 sin (2) over the interval…

A: Given that the region bounded by the functions  and  over the interval

Q: Determine the integral by making the appropriate substitution. 1 1+ 4e dx

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Q: Determine lim f(x) given the definition of f(x) below. (If the limit does not exist, enter DNE.)…

A: For finding, if f(x) is a polynomial, then for finding limit, we need to substitute a in f(x) and…

Q: Find the area of the region pictured below that is bounded by the functions v(y) = 3y – 6, u(y) =…

A: The region bounded by the curves  and .The aim is to find the area of the region by integrating…

Q: 256x The volume of a sphere is increasing at a rate of 8 cm³/sec. Find the rate of change of its…

A: The rate at which the volume of a sphere is changing, To determine: The rate of change of the…

Q: 6. Find the first term (a,) and the common difference (d) for the arithmetic sequence: S5 = -105, a5…

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Q: A patient has an illness that typically lasts about 24 hours. The temperature, T, in degrees…

A: Given that a patient has an illness that typically lasts about 24 hours. The temperature, T, in…

Q: Write an equation of the graph in the final position. The graph of y= 2* is shifted 4 units left and…

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Q: 5. Find two antiderivatives of f(x) = x0.8 - 3e²¹ + π cos(2x)

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Q: The compound amount, A, accrued with continuous compounding is given by A= P.100.4343rt, where P is…

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Q: Given the definitions of f(x) and g(x) below, find the value of g(ƒ(8)). f(x) = X 11 g(x) = x² + 7x…

A: The given functions  and .The aim is to find the value of .

Q: In 1619, the German astronomer Johannes Kepler showed that the square of the period of a planet (how…

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Q: The price-demand equation for a particular flashlight is given by p= 114 -0.004x, where x is the…

A: We need to find consumer and producer surplus.

Q: . If an item has a new cost of C and an annual depreciation rate of r (as a decimal), its value, V,…

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Q: a. 7* = 72 x b. 7 = x = 1 2401 * Preview Preview

A: To solve the following equations.

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: The objective of this question is to find the critical numbers of the given function f(x) = 12x -…

Q: Given f(x) = -√√/16 - x is concave up on its domain, what is an estimate for f (4.9) using the local…

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Q: 9. Suppose 0 < a <b, and Find the value of få f(x²)dx. A. 4 B. 2 C. 1 D. -5 [F(x²)dx=6₁ ["f(x²)dx =…

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Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. S² dt

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Q: ∞ 4. Apply the Ratio Test to the series [ the limit lim n→∞ (3n)! n=12¹ (n!)3 an+1 an and find

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Q: (5) Are there other shapes that would hold the same volume yet have even less surface area? Let's…

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Q: 1. Find the area bounded by x = y²; x = −2y² +3

A: To find the area bounded by

Q: TU Find the speed for c(t) = (3 sin(5t), 8 cos(5t)) at time t = FR

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: Solve the initial value problem below using the method of Laplace transforms. ty'' - ty' + y = 5,…

A: The initial value problem is given as,solve the problem.

Q: Please answer the below quaestions: If f(x)= g(x)/ x,  and g(x)= x + sinx  ( interval 0, 2π) Find…

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Q: Find functions f and g so that fog=H. 9 H(x) = (9x + 6) Choose the correct pair of functions. ..

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Q: Question 12 Determine the value of x(t) at t = 0 given its Laplace transform. Choose your answers…

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Q: 4. For the function fwhose graph is given, state the value of each quantity, if it exists. --2- 0…

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Q: A particular commodity has a price-supply equation given by p= 368(1.039), where x is the numbers of…

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Q: Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the…

A: The standard form equation of the vertical parabola:Where  is the coordinate of the vertex of the…

Q: Refer to the graph shown below and evaluate Ĵ 1941 CH - 4 f(t)dt.

A: Consider the figure

Q: The amount, A, of 159 grams of a certain radioactive material remaining after years can be found by…

A: Given that the amount A of 159 grams of a certain radioactive material remaining after t years is

Q: 2. Find the indefinite integrals. (You may want to differentiate to check, but it's not required) a)…

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Q: Tell whether the below piecewise function is  Undefined Continuous but not Differentiable…

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Q: Find the unit tangent vector T(t) at point P. r(t) = t²i + tj + 20 k, T(5)= X P(25, 5, 20/3) Find a…

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Q: Given the sequence an n>1 = n²-1 n+3 ' (a) List the first 5 terms of this sequence. Give exact…

A: The given sequence .The aim is to find the following values,(a) First five terms.(b) The value of…

Q: Find the average value of h(x) over the interval [1,7] given that g (z)=-6x + 8. Edit View Insert…

A: Given,

Q: JO 1/8 ន √1 16x2 dx

A: By change of variables to evaluate the following definite integrals.

Q: 17. The amount, A, of 108 grams of a certain radioactive material remaining after years can be found…

A: Given that the amount A of 108 grams of a certain radioactive material remaining after t years is

Q: Find the gradient field of the function, f(x,y,z) = (3x² + 2y² + z²) −1/².

A: According to Bartleby Guidelines, we can solve only first question from multiple question, please…

Q: Of all rectangles with a perimeter of 5, which one has the maximum area? (Give the dimensions.) The…

A: The area of a rectangle is:Where,l is the length of the rectangle.w is the width of the…

Q: Convert the Cartesian coordinate (-2,-5) to polar coordinates, 0 ≤ 0 < 2π r = Enter exact value. 0 =

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Q: 45-74. Definite integrals Use a change of variables or Table 5.6 to evaluate the following definite…

A: According to the bartleby guide line we do only first part of multiple questions.(46) Let assume,

Q: 2 sin(x) cos(x) + √3 sin(x) = 0 Find all angles in radians that satisfy the equation. For each…

A: The given equation is

Q: Find the value of (fog)' at the given value of x. Assume that f'(3)=8, g'(4) = -6, g(4)=3, and y =…

A: The chain rule of differentiation is given by