Calculate the iterated integral 5-x dx dy 2 х —1 and draw the region over which we are integrating.

Q: For the following functions find the nth Taylor polynomial centred around a. 1). f(x) = e, n = 4, n ...

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Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show ...

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Q: dy :-y = xy2 dx

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Q: dx x² Vx²-1 -2.

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Q: 5. Sxe*-* dx -et- +c Arcsin (3x²) + C 6. V1- 9x* 7. dx 1+x3 Arctar 3

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Q: -8 Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....

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Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2...

A: We will use the fact that  The Mean Value Theorem states that if a function f is continuous on the c...

Q: 4. Ifu = f(x), then : dx = J x* + 2x² + 1 k + C for some constant k. x² + 1 Compute kf (1). (a) ¼ (b...

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Q: y =2(2x+5) complete the below for x =-1/2,-1/5,0,1,2

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Q: A particle moves according to a law of motion s = f(t) t > 0, where t is measured in seconds and s i...

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

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Q: A function f(x) that is discontinuous at a point x = a in its domain may still have a limit that exi...

A: Given statement: A function f(x) that is discontinuous at a point x=a in its domain may still have a...

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

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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: Find the equation of the line through P = (8, 7) such that the triangle bounded by this line and the...

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Q: Find the first derivative of the given functions. A. Trigonometric Functions 1. y= sec? 0 – tan² ® 1...

A: As per our guideline we are supposed to be answer only A(questionp 1y& 2)part you can respost qu...

Q: 2. Solve example 2 of rational inequality. You can refer to example 1 for the gide steps Example 1 3...

A: Inequality

Q: y(x^2+y^2-1)dx+x(x^2+y^2+1)dy=0 solve using integrable combinations

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Q: Determine if the series converges or diverges. 00 Σ n=1 n! The series (coverges/diverges) using the ...

A: We have to find, the series is divergent or convergence. 

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: 2 cos(За? + 5) + [62? + 2] (а) lim За2 + 5 0)2

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Q: Evaluate the integral cot 2x Xp- Vcot2 2x - 15 -금ArCsec Csc 2x +C A 4 -nlcot 2x + Vcor 2x - 15|+C co...

A: This question is based on indefinite integral.

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: Enter the value of L- 1.27].

A: Floor value of x  is given as the greatest integer that is less than or equal to x

Q: e3x 2. Let dx be given . If u = e* + 1, then the resulting integral is ex + 1 | f(u) du. Compute f(3...

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Q: 1. The graph of a function f is shown. Verify that f satisfies the hypotheses of Rolle's Theorem on ...

A: Rolle's Theorem Let f(x) be a function that is continuous on [a, b]  and differentiable on (a, b). I...

Q: z° – 6z' + 4z – 2 dz |

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Q: Given: J5x2 cos(3x³) dx. If U=3x°, then the resulting integral is Jf(u) du. Find 4

A: I=∫ 5x2 cos(3x3) dxu=3x3du = 9 x2 dxx2 dx =du9which gives;I =∫ 5 cos(u) du9I =∫ 59cos(u)  du .....(1...

Q: Find h'(2), given that f(2) = -5, g(2) = 4, f'(2) = -2, and g'(2) = 3. %3D f(z) Express your answer ...

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Q: 1+ Inx 6. Find f(x) so that when u = f(x) the integral an( f(x)) dx can be rewritten as cot u du. (a...

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Q: IV. Constructing. Construct the table of values, graph the function and find the indicated limits ea...

A: 1. limx→+∞3x2. limx→-∞4x

Q: An object is dropped from a tower, 576 ft above the ground. The object's height above ground t secon...

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Q: (a) The eigenfunctions of the following eigenvalue problem: X" + XX = 0, X'(0) = X'(#) = 0 %3D are g...

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)5 f(x) = 8.

A: The given function,        f(x)=11+x5

Q: 16. u du Form Answer .Given: S 10% -dx а) 3 | а" du Find: formula b) | a"du c);| a*du d) =| a"du

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Q: du Form Answer u 10 20. Given: Tdx a) 3 a" du Find: formula b) | a"du c) a"du d) a"du

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Q: III. For each of the following functions, find the indicated derivative using the definition. Show s...

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one. ...

Q: Prove that lim (1 / n P ) = 0, p>0.

A: Given 

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

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Q: Write an equation for a rational function with the given characteristics. 4, x-intercepts at (-4,0) ...

A: Explained below 

Q: rectangular carpet has an area of 220 yd^2 .The width of w is 9 yards less that the length l.find th...

A: Options are wrong I have given you correct answer

Q: 1. An inverted conical tank with 14 m height and 6 m radius at the top is full of water. Calculate t...

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

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Q: according to the squeeze theorem, for values of x near a if g(x)≤f(x)≤h(x) and limx→ah(x) = L then l...

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Q: Give a power series Cnx" such that it is =1 convergent if |x| 1 of x = -1.

A: A series of the form {\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}=a_{0}-a_{1}+a_{2}-a_{3}+\cdo...

Q: Evaluate the integral V4x4 – 12x2 +7 xdx

A: Using integration of square root of x2 - a2 and follow step 2nd . 

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

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Q: 3. The integral of an t dx is b In|sec(In(2x)ª)|. What is b? A. 1/2 В. 1/4 с. 2 D. 4

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

A: Using Bernoulli equation. Follow step 2nd .