1. One of the partial fractions for 2 4x²+x-9 x3+2x²-3x 2 x+1 a) x23 b) x 1½ c) x² d) x-1 x is

Q: Complete the square and find the indefinite integral. (Remember to use absolute values where…

A: We solve the integral:I=∫x2−12x+27​x​dx Step 1: Complete the SquareThe quadratic expression in the…

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A: NOTE:-The term "sen" in the given equation refers to the sine function in Spanish and some other…

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Q: Show that the function f(x, y, z) = ex²+y²+z4 defined over the domain D = {(x, y)| x² + y² + z² =…

A: Given function: f(x,y,z)=ex4+y4+z4 defined over the domain: D={(x,y,z)∣x2+y2+z2=1}, has 6 global…

Q: Q8 Salve: f√coshx-i.dx do Solve: So Q₂ Qio Salve S Sinho + cosho dx 4-x2 Qll Solve Sdx √ex+1 Q12 If…

A: Step 1:Step 2:Step 3:Step 4:

Q: Total marks 15 པ་ (i) Sketch the trace of the following curve on R2, (t) = (t2 cos(t), t² sin(t)), t…

A: 5(i)(ii)L≈107.68(iii)

Q: x-4 Let f(x)=5x-1, h(x) = Find (fo h)(0). 3 (fo h)(0) = (Type an integer or a fraction.)

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Q: EXAMPLE 3 Find S X √√2-2x2 dx. SOLUTION Let u = 2 - 2x². Then du = Χ dx = 2- 2x² = 信 du dx, so x dx…

A: Question 1Explanation:   Question 2or,  ∫1+25x2tan−1(5x)​dx=101​(tan−1(5x))2+C

Q: O Prove that the function f(x, y) = (x² + y²)e-(x²+y²) has infinitely many critical points and…

A: Prove that the function  f(x,y)=(x2+y2)e−(x2+y2) has infinitely many critical points and classify…

Q: 60! 5!.7!.15!.33!

A: The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers…

Q: If f(n) (0) (n + 1)! for n = 0, 1, 2, ..., find the Maclaurin series for f. CO Σ n = 0 Find its…

A: We are given:  f(n)(0)=(n+1)!We find the Maclaurin series for f(x). The general formula for the…

Q: #9

A: Step 1:Step 2:Step 3: Step 4:

Q: 1 1+x 26. Derive the formula: tanhx=-In- 2 1-x ; x<1

A: Ans 26 page 1:Ans 26 page 2:

Q: Show that sinh(A+B) = SinhA. cosh B + Cosh A. sinh B Find y if y = x++ Solve; -e* dx exxex Solve:…

A: 1. Show that: sinh(A+B) = sinhA coshB + coshA sinhBProof:We can use the exponential definitions of…

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A: To find the average velocity over the interval [1 , 5], we use the formula:vav = (s(t2) - s(t1)) /…

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Q: (1) (4 points) Give a parametrization c: R R³ of the line through the points P = (1,0,-1) and Q =…

A: Step 1:Step 2: Step 3: Step 4:

Q: 2. Which of the following differential equations has the direction field shown? Explain your answer…

A: May this answer helpful to you.

Q: • -7 10 1.0 (2 - x) for 0 < x < 2, Let f(x) = for 2< x < 6. Compute the Fourier cosine coefficients…

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Q: Find the distance from the point (-9, -3, 0) to the line ä(t) = (−4, 1, −1)t + (0, 1, −3) .

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Q: Example: Solve (x − 1)y" + 2y′ = 0 around x0 = 0. -

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Q: Let (5,3,-7) and = (2, -3, -6). = Compute the following: u× u = -4(u xv) ux (-4v) (+v) × v=

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Q: 1. Evaluate the limit. Show all steps and simplify answers. lim 7x - 4ex x+2x+5ex

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Q: Find the slope of the line secant to the curve F(x) = 13-x³ (from x=1 to x=2]

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Q: Use the product rule to find the derivative of the following. p(y) (y¹ + y²) (6y¯³-10y¯4)

A: Step 1: Step 2: Step 3: Step 4:

Q: The expression 3 | (3+1/+1) of the following integrals? A Ов E + + + + 18 3+1+1 3++1 3++1 (A) √2×14…

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Q: Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x…

A: Given: f(x)=3(x−1)21−cos(4x−4)​; a=1 (a) Here, We required to draw the graph of f(x) by using any…

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A: Step 1:Step 2: Step 3: Step 4:

Q: 1. The parametric equations x = u, y = u cos v, z = usin v, with Ou≤ 2, 0 ≤ v ≤ 2π represent the…

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Q: 10 pls

A: Here is the step-by-step explanation:We will solve each problem step by step, using the relationship…

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Q: Find the one sided limit 2 lim Flx) where f(x) = (x²-4_x<l X73- 2 34-x² 1<x<3 3x-1 358

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Q: A sequence is given by the formula an = n/2n^2 +1 . Show the sequence is monotone decreasing for n…

A: StrategyTo prove the sequence is monotone decreasing, we need to show: an​ &gt; an+1​  for all…

Q: 5. Construct a (2 × 2) matrix that performs the following linear transformations, in order, at once:…

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Q: #8 (a) Find the equation of the tangent line to y = √x+3 at x=6 (b) Find the differential dy at y =…

A: If you have any problem let me know in the comment section thank you.

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A: The given function is:y=4x4​+8x21​ The formula for finding the arc length of a curve in rectangular…

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by x…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: 8:37 ▬▬▬▬▬▬▬▬▬ Ο Graph of f The figure shows the graph of a periodic function f in the xy-plane.…

A: To determine the frequency of a periodic frunction from a graph, follow the steps below: Step 1:…

Q: Keity x२ 1. (i) Identify which of the following subsets of R2 are open and which are not. (a) A =…

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Q: If f(x)=x2+4, g(x)=x-6, h(x)=sq root of x, then (f o g o h)(x)=

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Q: V. Consider the power series Σ (-2x-1)" (5)²+n n=1 1. Show that the series obtained when x = 2 is…

A: First, we substitute the given value of x = 2 into the power series. The power series…

Q: Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6…

A: Approach to solving the question: Detailed explanation:Examples: Key references:

Q: Find the following limit or state that it does not exist. Assume b is a fixed real number. (x-b) 40…

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Q: 4. Consider the initial value problem y' = 3x(y-1) 1/3, y(xo) = yo. (a) For what points (co, yo)…

A: (Hope this helps)