Find the limit. (If an answer does not exist, enter DNE.) lim (x + Ax)² – 4(x + Ax) + 9 – (x² – 4x + 9) Дх | Ax→0

Q: Given that Vf(15, -6) = 4i – j, find the directional derivative of the function f at the point (15,…

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Q: ) Find of the implicit function a? + 5xy + y? – 2x + y – 6 = 0 at the point 1. . (1, 1).

A: Topic:- derivatives

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Q: An open box is to be made by cutting small squares from the corners of rectangular board and then…

A: let "x" be the length of the side of the square cut.Length= 8-2xWidth = 6-2xHeight =xVolume =…

Q: Flnd the maximum rate of change of f (x.y) =e*²+e*+2y at P (2,1) 29 e4 V 29 e 16 O 7e4 O Viet

A: gradient of function fx, y=ex2+ex+2y, at 2, 1

Q: 5. Evaluate the limit of (x^3-2x^2-x+2) /(x^2-4) as x approaches 2. a. a b. % с. 2/5 d. 4/7

A: Note: Since the student has posted multiple questions but first question (question number 4) is…

Q: 3. S sin³ 0 cos³ 0 d0

A: Given

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Q: Find the length of the curve r(t) = t^2i − 2√2tj + (t/2 − 1)k for 0 ≤ t ≤ 1.

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Q: Express the Cartesian coordinates (-3,1) in polar coordinates in at least two different ways. Write…

A: We have to convert in polar coordinates.

Q: BASIC CALCULUS 1. The line segment from (1, -1,3) to (0, –3, 1) forms a diameter of the sphere S1.…

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Q: Given the curve y = x' and the line y = 2 – x . M. Find the moment of R with respect to the x-axis…

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Q: A company has the following production function for a certain product P(x, y) = 27 x0.3 y0.7 . Find…

A: Given: So,        Px=∂ ∂ x27x0.3y0.7Treat y as a constant     =27y0.7∂ ∂ xx0.3     =27y0.7·…

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Q: Q.4 Let Ø be a scalar point function defined as follows Ø = x3 + y3 + z - 3xyz. %3D 4.1 Find the…

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Q: * This equation is an example for linear equations dy y + dx = x²e* False O True O

A: To determine whether the given statement is True or False.This equation is an example for linear…

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Q: dx In x +1+ Vx² + 2x| + C Vx2 + 2x

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Q: This equation is. . .differential equation dy y2 = X x² + dx ху Bernoulli Separable Homogenous…

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Q: Where is each function continuous? (b) f(r) = sin-(1-r) %3D I+3 (c) f(r) In ) %3D (d) f(r)= 12+5r+ 6

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Q: 9. Evaluate the limit of (x-2)(x^3-8) as x approaches 2. а. а b. 1/12 с. 0 d. 2/3

A: As per our guidelines we are supposed to answer?️ only 1 question. Kindly repost other question as…

Q: circumference C of a circle is a function of its radius given by C (r) = 2r. xpress the radius of a…

A: Topic:- function

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Q: Q2/: Full the following blanks by the suitable solution (Undetermined Coefficients method) If y" +…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t? + 4 1 lim 5t2 + 6 7t (?,?)

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Q: 15. ſ sin² 3t cos 3t dt

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Q: 2 tan(x)dx

A: This question is related to definite integration, we will solve it using given using given…

Q: 99. Find the point of inflection of the curve y=(9x^2-x^3+6)/6. a. 3,10 b. 2,8 с. 3,8 d. 2,10 100.…

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Q: Find the nth term of  (– 4 3 14 29 ) and (4, 5, 8, 13)

A: Sequence

Q: From Rogawski ET 2e section 8.4, exercise 1. Calculate the Taylor polynomials T2(x) and T3(x)…

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Q: A gasoline tank is in the shape of a right circular cylinder (lying on its side) of length 14 ft and…

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Q: taylor tanox)

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Q: 3 4x Evaluate -dx. 4 2 x'-6 3 4x -dx = x* -6 4 (Round to the nearest thousandth.)

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Q: taylor tan)

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Q: 2 2 Find the sum of the series E Vn +4 yn+5 n= 1 The sum of the series is (Type an exact answer,…

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Q: Find a cartesian equation for the curve r2 cos(20) = 4. Equation Use your answer above to identify…

A: Use the formula for conversion from polar to Cartesian coordinate.

Q: Find the inverse of the function on the given domain. f(z) = (x – 14)2. [14, 0) f-1 (2) =

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Q: Use function composition to determine if f (x) and g (æ) are inverse functions. f (x) = Vx+I and g…

A: f(x)= x+13g(x)=x3+1Let y=f(x)y=x+13cubing on both sidesy3=x+1x=y3-1since y=f(x), so…

Q: ICLO-1) Three players (Ady, Brenden, and Cara) are sharing a pie that is worth $15. Suppose that the…

A: This is a problem related to percentage. Based on the general formula and concepts we will answer…

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Q: This equation is an example for linear equations dy y + dx x²e* False O True O

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Q: 9. S sec³ x tan x dx

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Q: Write an expression for the nth term of the geometric sequence. Then find the i a, = 8, r = n = 10…

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t=0 %3D 1 1 1 T(0) %3D V3…

A: Let's find.