Use the differential to approximate the expression. Then use a calculator to approximate the quantity, and give the absolute value of the difference in the two results to four decimal places. /112 What is the value found using the differential? V112 =O (Round to four decimal places as needed.)

Q: dy Use implicit differentiation to find dx 2х - 3 5y? 2x +3 dy dx

A:

Q: Solve the given VSDE dy/x − y (dx/x^2) = 0

A: Solution: As per given data,  dy/x − y (dx/x^2) = 0 we solve by variable separable method In that…

Q: 7) Find all the second partial derivatives of f(x,y) = x³y% + 2aªy.

A: Second derivative

Q: Find the cofactor matrix of the following matrix 1 0 1 A = 4 -2 5 1

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Q: If f(x, y) = 16 − 4x^2 − y^2 , find fx(1, 2) and fy(1, 2) and interpret these numbers as slopes.…

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: Question 17 Write the vector v in terms of i and j whose magnitude Iv and direction angle 0 are…

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Q: Problem #2: Differentiate f(x) = [(3x* – 5)(2x³ + 9x – 6)]° and solve f '(2). Solution: Reason:

A: Solve the following

Q: Question 2 (. Consider the function f(x) = %3D a2+1 (a) Find the intercepts of the graph of f (if…

A: As per guidelines, I can answer maximum three subparts of a question. Since there are multiple…

Q: = e3 + C is the general solution to the differential equation: y' = 3y. Select one: O True O False

A: We need to choose correct option.

Q: The value of E +2i+1 is i-1 139 146 124 90

A: Solving

Q: Find the curve length of the function 1 1. f(x) = ;x² 0 < x < 3

A: We can find the curve length as below.

Q: the Area that lies inside r=3+2 sin 0 out side r=2 is

A:

Q: A) lim x→3−    f(x)= B) lim  x→3+    f(x)= C) f(3)= D) Determine whether the function f is…

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Q: Test the series for convergence or divergence using the Alternating Series Test. ∞ (−1)n 7n + 1   n…

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Q: Question 25 Find the standard form of the equation of the parabola using the information given.…

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Q: A 17-ft ladder is leaning against a wall. The foot of this ladder is sliding away at the rate of…

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Q: Evalute The Line integral of The Fiel f=xi+zj+yK o ver The helix rz cost i +sintjt tK for osts I

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Q: man wishes to use 100 feet of fencing to enclose a rectangular garden. Determine the maximum…

A: Given query is to find the maximum possible area.

Q: df df Calculate the first order partial derivatives and find and dy dx f (х, у) %3D (ху — 1)2

A:

Q: Use a change of variables to find the indefinite integral. Check your work by differentiation. 1 xp-…

A: solution:-∫11-4x2 dx=let x=12sintdx=12cost dt∫11-4x2 dx=∫11-412sint2 ·12cost dt=∫11-sin2t ·12cost…

Q: If f(æ) = 8 sin-(*), then f (2) =

A:

Q: Find the work done by F over the curve in the direction of increasing t. Work means line integral F…

A: To find the work done in both the given cases.

Q: Solve the system by the method of substitution. (If there is no solution, enter NO SOLUTION.) ** =…

A:

Q: 3. Compute the area bounded by the limacon r(0) =1+2sin 0 excluding the area of the inner loop.

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Q: Use the Squeeze Theorem to show that lim x* cos = 0. If If(x) < B| for all x in an interval…

A: Squeeze (Sandwich)Theorem The Sandwich Theorem, also known as the squeeze theorem, is used to find…

Q: 4 Consider the following geometric series: 2 + 8. 16 + ... Identify a and r, find a formula for the…

A: solution:-2+43+89+1627+...first term, a=2common ratio, r=8943=23general term, an=arn…

Q: Let f(x) = (4sin z + 2 cos z)arctan z f (x) =

A:

Q: dy Find for y = tan-(3z) de Ans=

A: A detailed solution is given below.

Q: If the differential equation ydx+xdy= 0 is being solved, what is the geometrical figure represented…

A: Differential equations

Q: 2. Find the volume of tetraherdon with the vertices A(-1, 2,0), B(0,3,-1), C(3,3,0), and D(1,1,-1).…

A:

Q: Given that f(x) = x² - 5x + 6, evaluate the function fla +b) - fla). 2a+b-5 b-5 2a+b+1

A: Simplify the expression for the given value of x

Q: 3- A box with an open top is to be constructed from a square piece of cardboard, 3m wide , by…

A:

Q: Problem #2: Differentiate f(x) = [(4x³ – 1)(8x² + 6x – 3)]° and solve f'(2). %3D Solution: Reason:

A: To differentiate the given function.

Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per…

A:

Q: Evaluate the following expressions. Your answers must be exact and in simplest form. (a) In e l = -1…

A: We can answer the questions as below.

Q: 00 n2+9 E(-1)"-1 n2+ 8 n=1 a) Show that the ratio test fails b) Test the given series for…

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Q: D) 1. Which of the following is the antiderivative of f(x) = x' + x +1? A) 3x +2x + C C) x' + x +x +…

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Q: A population of bacteria is growing according to the equation P(t) = 2000e0.05t. Estimate when the…

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Q: Estimate the area under the graph of f(x) : 1 over the interval [0, 4] using five approximating x +1…

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Q: Ion 14 Based on the graph, find the set of all x-values for which the points P(x, y) are on the…

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Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: Which of the following is the particular solution of the differential equation dy = e ;y = 1, when x…

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Q: The graphs of the first and second derivatives of a function y = f (x) are given below. According to…

A: Solve the following

Q: 12. Let y = 4x-4x+3. %3D (a) Find the equation of the tangent line to the graph of the function at…

A: Solve the following

Q: a2– x2 (x+y)dæ dy

A:

Q: Sx² sec² x³ dx .2

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Q: Find the integrals by the method of partial fractions. x² – 3x + 4 dx ·J (a +1)(x – 1)(r+2) 1. 5х —…

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Q: During its first season, the number of viewers who watched the new television programn can be…

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Q: Write the vector v in terms of i and j whose magnitude Iv] and direction angle 0 are given. Ivl - 7,…

A: This question can be solved using the concept of component form of vectors.