d²y Q2: find of the following statement dx2 a) y = xcosnx b) y = In x3 + ex + cot x

Q: dx S 9x2+16

A: We have to solve integration.

Q: 3.

A: ∫x41-x2dxPerform trignometric substitutionSubstitute…

Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and -e sin(x+y) which if the %3D ay following is…

A: On solving this we will get:- Option (A) is correct.

Q: x+1 8. -dx (x-1)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: S(1 + tanx)² dx

A:

Q: completely

A: We will solve the integration.

Q: Find V· (F x G), if F(x, y, z) = 11xi+j+ 4yk and G(x, y, z) = xi+ yj – zk. V· (F × G)

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: Cives f(x.g) = メー2メラーリメy+5 Find the Ccritical points oo f and all detevmine the nature of each of…

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Q: A Find the area bounded by the curves, the axis and the given values of x. Sketch the graph. 1.…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: This question can be solved using the concept of domain and of functions and value of a function at…

Q: Question 2 x2 Consider the function f(x) = x² –1 " (a) Find the intercepts of the graph of f (if…

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Q: s @ = 135° a solution to the equation sine = cos 0. Justify your answer and explain the approach you…

A: Given query is to find that statement is true or not.

Q: Determine if the given series is absolutely convergent, conditionally convergent, or divergent. Show…

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Q: Find the sum of the series. 1 - In(4) + (In(4))² _ (In(4))³ 2! 3!

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Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x² – 9…

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Q: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³+ 6x d. h(x)…

A: Given data

Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is the last two digits…

A: Permutation: Permutation:  The permutation is a method of arranging objects in a specific order.…

Q: Explain why the integral is improper. 18 .6 1.4 1.2 y F0.8 F0.6 F0.4 F0.2 -2 -1.5 -1 -0.5 At least…

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Q: 7.372 The rate of change of the weight of a mouse, can be modeled by r(t) grams per week, where t t…

A:

Q: 5) Find tue soletion of the differen tiel equation dr Sec't which paffes dt fant +1 turough the…

A: Solve the differential equation by separation of variables.

Q: F. Change the Cartesian integral to polar coordinate 11-y !! (x² +y*)dx dy

A:

Q: Cosx dx Vi+sinx

A: Given :∫cosx1+sinxdx

Q: tdt 1-t4

A: Topic = Integration

Q: Find r'(t). r(t) = (tan¬(11t))i+t cos(t)j – vik NOTE: Enter your answer in terms of i, j, and k.…

A: This is a problem related to derivative of the function. Based on the general formula and concepts…

Q: Evaluate the definite integral. O e10 e10 - 1 i+ k 10 10 - 1) j+ k 1- e10 - 1 10 e10 i - e j+ 1 k 2…

A:

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: 1. For the autonomous differential equation = y(4 – y²) find the equi- librium solutions and…

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Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

A: Limit

Q: 3 roblem 4. The third term of a geometric sequence is 9, and the common ratio is Find the fifth…

A: Given problem:- The third term of a geometric sequence is 9, and the common ratio is 3/2   Find the…

Q: In which limits below can we use L'Hospital's Rule? x – 2 lim 1→2 In(3 – æ) 1- et lim 2-0 sin(5x)…

A:

Q: Find the minimum speed of a particle with trajectory c(t) = (t3 – 4t, t2 + 1) for t > 0. Hint: it is…

A:

Q: 1. S 2xe2*dx

A: Given that,   Using integration by part

Q: Find r'(t). r(t) = (tan (6t))i+t cos(t)j – Vik I| NOTE: Enter your answer in terms of i, j, and k.…

A:

Q: Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt' the product directly and…

A: r1(t)=cos⁡(t)i+sin⁡(t)j+6tk,r2(t)=5i+tk Given:  ddtr1(t)⋅r2(t)=r1(t)⋅dr2dt+dr1dt⋅r2(t) and…

Q: dt 1-cos t+sin t

A: First we shall simplify the expression then integrate

Q: Find V x (V x F) if F(x, y, z) = 5xyj+7xyz k. %3D V × (V × F)

A: Curl vector

Q: o) rind all veluees of x for which fue Canveryes. for there helues of x, wnite tul fum of tue senes…

A:

Q: Find the limit. 421 (a) lim 7+ 17 (b) lim x-0 X 3

A: Topic = Limits

Q: 1- x2 If f(x) = then f'(x) = x² + 1 2/x(x² + 1)³

A: Given : f(x)=xx2+1   To Show: f'(x)=1-x22x(x2+1)3

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 00).…

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Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: Show that the function f defined by (x, y) = (1, – 1) f(x, y) = 1² + y (x, y) # (1, –1) I + Y is not…

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Q: Evaluate the following limit using Taylor series. 7 7 tan -(x) – 7x + lim 4x° 7 7 tan "(х) - 7x +-…

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Q: Solve the differential equation dy tan y x Cos x 3 dx

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Q: If we apply Rolle's Theorem to the function f(x) = 2x? – 4x – 7 on the interval [ – 1, 3], how many…

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Q: Calculate the limit of the following recursive sequence ao = 1 an+1 = V1+ an Hint: Prove that an is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Determine whether the series converges absolutely or conditionally, or diverges. (-1)" + 1 n + 8 n =…

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Q: FH is perpendicular to AC In the figure, AC is diameter. If EF = 3 and FG = 2. Find GH. E G EH is…

A: Similar triangles: Similar triangles are triangles with the same shape but different sizes. Similar…