Consider the function f(x)=√x near x = -1. Find the linear approximation error when using the linear approximation to estimate -0.75.

Q: Find the transform of the given function by use of a table. f(t) = 3e-4t sin 5t A B C D E F (s) =…

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Q: lim y³-y y+1 y2 – 1

A: Evaluate the limit limy→1y3-yy2-1

Q: m #2: If ƒ(x) − x³ [f(x)]=-2x-12 and f(1) = 2, find ƒ'(1). - oblem #2: Enter your answer symbolica…

A: Given:- fx-x3fx4=-2x-12

Q: Find the derivative of the vector function r(t) = ln(14-t²)i + √12 + tj - 4e5tk r' (t) = (

A: Given data÷ Find the derivative of vector function.

Q: C Find the domain range x and y intercepts, vertical and horizontal asymptotes, and zeroes of the…

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Q: KINR 2. Let R be the region bounded by the z-axis, y = sinx on [0,5], and z Using washer method,…

A: volume is =3.8157

Q: Select the correct graph of the derivative of the function f(x) given below. -4 -2 -2 -4 12 4 X

A: Solution: Given figure is

Q: Find the total area between the x-axis and the curve f(x)=√x-1 between x = -8 and x = 8. O O a.) 15…

A: The given curve is f(x)=x3-1 between the x=-8 to x=8   We have to find the area of the curve…

Q: In Exercises. , use an iterated integral to find the area of the region bounded by the graphs of the…

A: According to our guidelines,i can solve only first please reroute the remaining question.

Q: Consider the differential equation (DE) 5 j=4 x/+¹y(2) + x² (y(7))12 + xy"+y' = cos(2x). a) Its…

A: Given that we need to find the order degree and number of initial conditions for the given…

Q: Evaluate Answer: dt t² + t-30 S₁

A: ∫1t2+t-30dt

Q: Find the derivative dy/dx by implicit differentiation √x + y = 1 + x2y2                     (the…

A: Point to remember:- y is a function of x

Q: Test the series below for convergence using the Ratio Test. n+4 34n+-3 n= The limit of the ratio…

A: ∑n=1∞ n+434n+3

Q: r'(t), r"(t), r'(t) r"(t), and r'(t) r(t) = 2t²i - 5tj + 5t³k X

A: Topic:- application of derivatives in vector algebra

Q: Express u = (6, -2) as a linear combination of v = (1, 1) and w (1, 1) and w = (1, −1).

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Q: (e) lim I→∞ /9x4+3x+2 4x³+1 (f) lim [2x] x- 8. Verify each limit using the definition of limit. (a)…

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Solution

Q: = 2 2 x²-3

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Q: 2000 Find an exponential function of the form P(t) = yoekt to model the given data. 10) In 1985, the…

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Q: lim tan 5x x0 tan 8x

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Q: Tablet Service A monthly tablet plan costs $34.99. Itincludes 3 gigabytes of data and charges $15…

A: Given data:- The given monthly plan cost is $34.99  The given includes 3 gigabytes of data and…

Q: Decompose a = (4, -1,0) into parts parallel and perpendicular to b = (0, 1, 1). What is the…

A: I am attaching image so that you understand each and every step.

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function. x²+x-1 x² - 1…

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Q: Compute the divergence and the curl of the following vector field. V = x sin y î+ cos y ĵ + xyk

A: given vector field=xsiny, cosy, xy

Q: ƒ(x) = = (x + 1)(x+2) x² - 3

A: As we know that; The Sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Product rule:…

Q: Find the third derivative of f(x) = 3√x³-5cosx. 45 O f(x)= 4553 9 O f(x)= - O f(x)= 45 O f(x)= - 9…

A: It can be written as f(x)=3x3/4-5Cos(x)

Q: dx If z² = x² + y², t = 6, and dt. 5, find dz dt. when x = 4 and y = 2.

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Q: 9. Find the vertical and horizontal asymptotes of the following functions. (a) f(x) = 9x² - 4 2x2 X…

A: a) f(x)= (9x2-4)/(2x2-x) b) f(x)= (x2-3x4)/(x-1).

Q: In each of the graphs A-E below, a possible graph of f (2x) is given in blue on the same axis as the…

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Q: This set represents O a line O a half-plane, including the boundary O a half-plane, excluding the…

A: Solved below.

Q: Find all relative extrema of the function. (If an answer does not exist, enter DNE.) 1.9 g(x) = x² -…

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Q: Find the parametric equations for the tangent line to the curve at the point (0, 2, 1). Use the…

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Q: Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) g(2),…

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Q: Evaluate S² (ti + t²j + t³k)dt = i+ j+ k.

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Q: Find Mx, My, and (x, y) for the laminas of uniform density p bounded by the graphs of the equations.…

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Q: 2. Use the Method of Lagrange Multipliers to find the minimum and maximum values of the function…

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Q: f(mıy)= √(Y+1) ² (n+1) log (n-y)

A: A function is given and we have to find its domain and range. Domain is the all the input values to…

Q: Find the positive t when the vector →r(t)=⟨9t,9t2,9t2−23⟩ is perpendicular to →r'(t).

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Q: Determine, using the definition, the Laplace transform of the function f(t) =1+t.

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Q: oblem #3: Let f(x) = ln[1 + g(x)] where g(7) Do not include 'y' in your answer. Problem #3: =e6-1…

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Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t²k, u(t) = 5ti + t²j…

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Q: 1 -1 2 a-c c+1 ¹] | = -1 2 7 1 0 c-3 0 1 0 {][ a 0 0 2a -2b 1 1 0 1

A: To create a system of equations to solve the variables.

Q: The function C gives the cost, in dollars, to produce a particular product, where C (x) is the cost,…

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Q: Use the position function s(t) = -16t² + vot+s for free-falling objects. A ball is thrown straight…

A: The position function st=-16t2+v0t+s0 for free-falling objects. A ball is thrown straight down from…

Q: Use implicit differention to find an equation of the tangent line to the curve at the given point…

A: Derivative is the key for such problems

Q: 4) f(x) = (x³+3X4x+D сха X.

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Q: 3 Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: 2. Find the absolute maximum and minimum values of f(x, y) D = {(x, y): y ≥ x², y ≤ 4}. 3x² + 2y² -…

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Q: Use the rules of differentiation to find the derivative of the function. f(0) = 2 cos(8) - sin(0) 9…

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Q: Find Vw. = x² + y³ + z¹¹ NOTE: Give your answer in unit vector notation; that is, in terms of i, j,…

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