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Q: 1. dr (0) 플 (6) 를 + (a) (b) r + 2In|피 +c + In피 + c + 2x +c

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Q: dz dz 10. Compute for the following equation. and dx dy e*Y + xz? = 6xy*. *z° ||

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Q: 15. Find the area between the curves x = y? - 4 and x = 8- 2y.

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Q: What is phase line

A: A phase line is a qualitative behaviour of autonomous differential equation in a single variable dy/...

Q: In Exercises 47-62, use a sketch to find the exact value of each expression. 47. cos(sin £) 49. tan(...

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Q: Solve the differential equation with appropriate method. Finalize answer free of logarithm and fract...

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Q: Is the series divergent or convergent? With complete solution and explanation +o0 (-1)" n! n=1

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Q: 4. If u = f(x), then k +C for some constant k. dx = x* + 2x2 + 1 x² + 1 Compute kf (1). (a) 4 (b) – ...

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Q: D Express the interval in (a-k, a+R) aad 1 x.-alc.R I(3x+1)?(<!

A: |(3x+1)2| &lt;1 both side we take square roots |3x+1|&lt; +1 3x+1 &lt;+1 3x+1&lt;1    or    3x+1&lt;...

Q: A woman attached to a bungee cord jumps from a bridge that is 36 m above a river. Her height in mete...

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Q: -5 dx Evaluate 2х — 10 (а) — оо (c) 1/2 (d) 0 00

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Q: Use long division to find quotient  x3 + 2x + 4        x - 3

A: By using long division find quotientx3+2x+4x-3

Q: (b) Let u = u(x, y) and f and g be twice differentiable functions. Then, a general solution to the e...

A: The objective is to find the general solution u(x, y) .

Q: 19. Give the midpoint approximation of xdx with n = 2.

A: Here, to approximate the given integral ∫04x3dx  using midpoint approximation with n=2. Let, f(x)=x3...

Q: 11-14 Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given inter...

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Q: dx reduces to du The integral 3. ex + 1 where u = f(x) and for some и constant k . Compute f(1). (a)...

A: Given

Q: The average student enrolled in the 20-week Court Reporting I course at the American Institute of Co...

A: Given query is to find the function N(t).

Q: Find the Taylor polynomials of orders n = 0.1, 2, 3. and 4 about x = 20 and then find the nth Taylor...

A: f(x)=2xx0=-1

Q: Exact Equations (w3 + wz? – z) dw + (23 + w²z - w) dz = 0 O (w? + z?) = 4wz + c O (w? + 2?) = (4wz +...

A: Given the exact differential equation(w3+wz2−z)dw+(z3+w2z−w)dz=0

Q: Consider the improper integral I = dz. 4x +1 (a) Find the value of the constant C for which the inte...

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Q: Use sigma notation to write the Maclaurin’s series for the function  f(x)=xcosx. Show complete solut...

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Q: Consider the function f(x) = 4x - 4x – 1 and complete parts (a) through (c). (a) Find f(a + h); f(a ...

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Q: n+ In (3) Given the sequence Then the limit lim a = a n- 00

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

A: Solution is here

Q: Use sigma notation to write the Taylor series about x = xo for the function. e*; xo = 6 6 2r – 6)* k...

A: Here we have to use sigma notation to write the Taylor series about x=x0 for the function f(x)=ex; x...

Q: Use sigma notation to write the Maclaurin series for the function 11 In(1 + x) Σ

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Q: Find g' (3) given that f(3) = -6 and f'(3) = 4 %3D (a) For g(x) = 3xr² – 5 f(x) %3D 1 g' (3) = %3D 2...

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Q: Instructions: Use Rules of Differentiation to differentiate the following functions. Show your solut...

A: Using product and division rule for differentiation. 

Q: 3. A single-input, single-output system has the state variable representation *= Ax + Bu y = Cx 1 wh...

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Q: u du Form Answer Ex. S 3+ 2cosx 5sinx 5 -5V3+ 2cosx + C dx 3+ 2cosx -2sinxdx ī du 3 15. Given: S -dx...

A: This is a integration problem

Q: dx The integral can be rewritten as -∞ V1 – x (a) lim (-2+2vī1-s) (b) lim (-1+ 2v1 – s S--00 S--00 (...

A: Given ∫-∞0dx1-x Let t=1-x differentiating with respect to x, dt=-dx ∫-∞0dx1-x=-∫-∞0dtt=-∫-∞0(t)-1/2 ...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) In(x), n = 4, c = 3 PĄ(x)

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Q: Evaluate the integral dx 2xx - 3x? A -In 4 V2x + V3 +C 1 V3+ 2x B In +C 2/3 V3-2 +C In 2/3 "/7x + /3...

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Q: Part of the piecewise-defined function (x – 1) + 2 if 0 < ¤ < 3 f(x) = b if x = 3 mx if 3 < x < 6 is...

A: Given problem:-

Q: 2022" + n 2022 (d) lim sin 2022! + n!

A: We have to find: limn→∞sin2022n+n20222022!+n!. We can take the limit inside of sin as the limit is o...

Q: dx du The integral , reduces to k=, where u = f(x) and for some ex + 1 constant k . Compute f (1). e...

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Q: In3 ex i. dx In2 4- ex i. X/16 - Inx e 1 iI. i xInx In2 1 dx Ino.5 e2x + 1 iv.

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Q: 5. Consider the function below. Is g continuous on (0,1]? on (4,1)? Why or why not? if x 4.

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Q: C) Replace the following polar equation by equivalent Cartesian equation. rsine Inr + In cose %3D

A: We can replace the given polar equation by equivalent Cartesian equation as below.

Q: Evaluate the following. Use the graph of f(x) to evaluate the following expressions. (4, 5) (1,5), (...

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Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: Evaluate the integral cot 2x V cot? 2x - 15 13. -순사 Csc 2x +C -Arcsec 4 А. Arcsec Csc 2x +C 4 1 Arcs...

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Q: Learning Task 3: Find the equation of the tangent line to the following curves at a given point 1. y...

A: we need to find the tangent line of y=x2-6x+9 at x=2

Q: 2. Summation (a) Write the sum 50+ 51 +52+..+ 99+ 100 in summation notation. (b) Compute the value o...

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Q: 2. Consider the following graph. 2- -2- What is the equation of the asymptote present? A. y=3 В. х%3...

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Q: Consider ſ* xe-**dx. What will be the appropriate solution and answer to this improper integral? lim...

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Q: Evaluate the integral tan 4x dx Vtan? 4x - 24 tan 4x 1 Arcsec 4/24 V24 +C O 1 sec 4x Arcsec 20 + C O...

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum...

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Q: A certain index I is a measure of soil moisture. An article described the rate of change of I with r...

A: dIdW=0.0634.6-I  

Q: dx The integral can be rewritten as - X (a) lim (-2 + 2V1-s) (b) lim (-1+ 2v1 -s) S-00 00--S (c) lim...

A: First we solve integral, put √1-x=t  And follow step 2nd .