Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x) = e4x, c = 0 f(x) = Σ n = 0

Q: u du Form Answer 5sinx dx Ex. J a+ 2cOsx 3+ 2cosx -2sinxdx uż du -5V3 + 2cosx + C 3 15. Given: •dx 5...

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Q: f = f (x, y) = u? + 3v, y = uv

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Q: dz 4z+z' ,2

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Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

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Q: Find the solution of the following initial value problem: An 14a,-1- 49an- 2; ao = 0, a1 = 6 %3D an ...

A: Let us take an=rn. So, the characteristics equation will be       r2-14r+49=0⇒r=7, 7 Further, we hav...

Q: 45-56 Find the absolute maximum and absolute minimum values of f on the given interval. 45. f(x) = 1...

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Q: az dz 10. Compute and for the following equation. dy ,3 eY + xz2 6xy*z³ %D

A: The given equation is: ezy+xz2=6xy4z3...(1)

Q: If inflation grows continuously at a rate of 6% per year, how long will it take for $8 to lose half ...

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Q: 2. Let dx be given . If u = e* + 1, then the resulting integral is F(u) du. Compute f(3). (a) 2/3 (b...

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Q: Evaluate the integral [/4x4 – 12x² +7 xdx (2x2 – 3)/4x4 – 12x² +7 – 2ln|2x2 /4x4 – 12x² + 7|} + c -3...

A: Given that, The integral is following, I = ∫4x4-12x2+7xdx We have to solve this integral.

Q: dy :-y = xy2 dx

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Q: sec (In x) + sec2(In x) tan(In x) 2х Given: dx Find: du tan(in x) 2х sec³(In x) + sec²(In x) sec(in ...

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Q: Csc X Given: dx Vcor?(글씨)-4cor(글씨)+4 -x)+4 Find: u ct 1 cot2 1 x) - 4cotx) +4 cot cor()- acot( X+ 4

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Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: Find the laylar polynomials of orders = 0,1,2,3, and 4 about x = No, and then find the nth laylor po...

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Q: 1 6. Evaluate the given integral using suitable substituion COs(V도+ 3) dr

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Q: Let S be the plane defined by 5x-Sy+10z 0, and let T be the plane defined by 2x-2y+5z=-2. Find the v...

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

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Q: 3. (3 marks) Given that u(x, y) = f(y- a) +g(y +x) is a general solution to Uzz = Uyy, %3D for twice...

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Q: 4 tanz dr 2. The value of the definite integral (b) (e) 1- (d) 0 (a) 1

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Q: SV1+ vw_dw

A: ∫1+wdw  

Q: Find the rate of change of the volume of a cube with respect to the length of its side s when s =3 ...

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Q: Evaluate the iterated integral by converting to polar coordinates. V2x – x2 5/x2 + y² dy dx

A: Explained below 

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 integral dx 2x3 - 3x x |/3x - /2 2/2"V3x + v2 1 +C O 16V2 + V3 In 3 |/2 - 3x +C In +C 2...

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Q: From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for ...

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Q: Use sigma notation to write the Maclaurin's series for the function f(x) = x cosx. Show complete sol...

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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: Find the radius of convergence of the power series. (If you need to use o or -0o, enter INFINITY or ...

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Q: 1 x + 3

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Q: Find the solution of the following initial value problem: an = 14a,-1 – 49a, 2; ao = 0, a1 = 6 %3D a...

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Q: 1. Consider the integral | 2nx g(x) dx . There is a function g(x) such that when u = In x the result...

A: The given integral is ∫2ln(x)g(x) dx. We have to find the value of g(3). Given that when u=ln(x) the...

Q: At 9 AM, ship B is 65 miles due east of another ship A. Ship B is then sailing due west at | 10 mi/h...

A: Given

Q: dw In each of the following, find dr and ds using the Chain Rule. 1. w = xy + yz+2z; x =r+s+t; y =rs...

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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 . 

Q: 37. h(t) = 14 -214 39. F(x) = x" (x - 4)²

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Q: Find the interval of convergence of the power series. (Be sure to Include a check for convergence at...

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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: -In 3 e* In 2 V4 - e*

A: As per our guidelines we are supposed to answer only one question i.e. the first question. For the s...

Q: dx The integral can be rewritten as 1- x (a) lim (-2+ 2v1-s) (b) lim (-1+2vī-s) S--0 (c) lim (-2+v1–...

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Q: Solve the following differential equations. Indicate the (Differential Equations) nethod/s used at t...

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, Y...

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Q: Solve the differential equation with appropriate method. Finalize answer free of Logarithms and frac...

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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: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

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Q: JUX² +2x-8 dx Evaluate lx + 1Wx + 1)* + 9 = l(x + 1) + Vtx + 1}² – 9|]+c 9ln (+ 1)/(x + 1)² – 9 – 3l...

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Q: 15. Find dr/d0: r = 4 – 02 sin 0 а. 20 sin @ - ө2 cos @ b. 0 cos e – 0² sin e - c. O sin e – 02 cos ...

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Q: 11. The integral of tan(In|4x²|) dx is bln|sec(ln(2x)ª)|. What is b? А. 2 В. 1 D. ! С.4 4

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Q: Calculate (1+ cos(y²))dA,where D is the triangular region with vertices(0, 0). (–2 - Vĩ,2· VT) e (0,...

A: Given problem:-

Q: How many ways are there to represent a function? Find the domain of the following function x²+3x+1 V...

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