...... 6,7 Solve both questions plz these are just mcqs type questions so plz

Q: Consider the integral I = fa x arctan(x) dx. (a) Write explicitly an approximation for I using the…

A: As per the question we are given the definite integral of x arctan(x) from x = 0 to x = 1 And we…

Q: Asap plz

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Q: Prove using mathematical induction. Show your solution. Prove 3 + 7 + 11 + … + (4n – 1) = n(2n + 1)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (5) Write the following second order ODE d'r dt² 0= a system of 2 first-order ODES: 2 a³ (dr m dt…

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Q: Find the arc length of the curve y = ln(x) between x = 0 and x = √3 Determine whether the following…

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Q: 24. If P(An) ≥ e > 0, for all large n, then P (An i.o.) ≥ €.

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Q: Can you use the method of partial fractions

A: We have  ∫180-x60-xdx=k∫dt We have to solve using partial fraction. Let 180-x60-x=A80-x+B60-x

Q: Get the function in algebraic form, state its representation in terms of the function unit step and…

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Q: Use spherical coordinates to find the volume of the solid enclosed by z = 2x² + y² and z = 12 - x² -…

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Q: Give a solved problem on Volumes of solids of revolution using Circular Disk Method. Show complete…

A: Circular disk method is also known as disk washer method.Answer given below

Q: Determine whether each of the following series (Sum from 1 to infinity) are absolutely convergent,…

A: As per the question we are given three different infinite sums from 1 to infinity And we have to…

Q: Expand f(z) = 1 (z-1)(z-2) -; 0<z-1|<1.

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Q: 11. Find the Taylor series at c = 2 for the function, f(x)= = formula for the general term. You need…

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Q: The following subsets A, B, and C of RX R are relations on R. Sketch the set. (i) B = {(x, y): [x] +…

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Q: Use L'Hospital's Rule to evaluate the following limits. ex-1 a) lim (x²-x³)e²x b) lim X118 x−0 tanx…

A: Given, a) limx→∞ (x2-x3)e2x b) limx→0 ex-1tanx c) limx→(π2)- (tanx)cosx We have to evaluate the…

Q: ²+ b² + c²p²-2(ab + bc+c

A: Part a

Q: a Consider the matrices A = 1 1 U = g h 1 b b |, V = X 0 a d,B= 0 C 1 1 d C h [f g 0 and X = y. If…

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Q: t²y" +ty' + t²y = 0 con y(0) = 1 y y'(0) = 0

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Q: What is the volume of a right circular cylinder with its base's diameter of 19.5 and height of 14.9?…

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Q: Consider the following equivalence relation on RK \ {U}: x ~ y if and only if x = A.y for some λ =…

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Q: QUESTION 42 A "whispering room" is one with an elliptically-arched ceiling. If someone stands at one…

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Q: 1) The dimension of the subspace of P3 consisting of all vectors of the form at³+bt2 + ct+d, where b…

A: We have to find the dimension of the subspace of P3 which consists the vector at3+bt2+ct+d   where…

Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

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Q: 6. SET UP the double integral which gives the volume of the solid in the first octant enclosed by…

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Q: x₁ 3 7 9 10 168 120 72 63 Given the table about the function f(x). Construct the Divided Difference…

A: Divided difference table:

Q: Consider the vector field ♬ = (x³y¹, x¹y³). The vector field is not conservative The vector field is…

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Q: Q2. Obtain the Fourier series for the function given in the diagram below f(x) 2 20 0 2T 3T X -2

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Q: QUESTION 3 (a) Consider the nonlinear equation A graph of the function is shown here. -est -1.5 -24…

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Q: Consider the three vectors 3 --)--(C)--0) 3 W = 9 -3 u= -2 3 Let S denote the one dimensional…

A: As per the question we are given three vectors u, v, w and S is the one dimensional subspace spanned…

Q: • Prove that |P(N)|≥ |R|, where P(N) is the set of all subsets of N.

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Q: Strontium-90 is a radioactive material that decays according to the function A(t) = Age-0.0244t,…

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Q: Evaluate the double integral 2x. 1 J₁₂ (2² + 3²) ²² dA, where D is the circular region inside x² +…

A: We will use polar co ordinate system to find value of double integral .  Note :only one question is…

Q: Please answer this correclty and I will give a thumbs up, thank you!

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Q: (Ctrl) Analyze completely (determine all the characteristics of the function from the domain to how…

A: We will use   relation between f , f' and f" to find characteristics of f(x) and then  draw the…

Q: Consider the following differential equation to be solved by the method of undetermined…

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Q: Determine which theorem applies to simplify the following. It is possible that more than one will…

A: Given  Find the work done by the vector field Fx,y,z=yzcosxyi^+xzcosxyj^+sinxyk^ along the…

Q: Find the maximum and minimum values of the function f(x, y) x²y subject to 4x² + 2y² Please show…

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Q: State whether each of the following random variables is discrete or continuous 1. The number of…

A: 1. The number of defective tires on a car Discrete 2. The body temperature of a hospital…

Q: 7. Given three points in the plane A, B and C and distances from each of these points to a 4th point…

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Q: The volume of the solid obtained by rotating the region bounded by about the line = 5 can be…

A: The volume of the solid is obtained by rotating  the region bounded by y=x2, y=5x about the line x=5

Q: Find the numerical value if a = 2x+y² 5y-x² 2/+ (%)³ and y ==

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Q: The set of degree 2 polynomials at²+bt+c, where c is even ; is a subspace of P2. a. True b. False c.…

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Q: Let C be the ellipse given by ² + y² = 1. () Find a polar equation for C. () Find a parametrization…

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Q: 16.4 Euler's Method 16-23 In Exercises 5-10, find the orthogonal trajectories of the family of…

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Q: Determine whether the following series converges or diverges. Be sure to state why it converges or…

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Q: If f+g is are differentiable at x0, then prove f and g differentiable at x0 ww

A: We are given that the function (f+g) is differentiable at x0. one has to show that f and g both will…

Q: You need to provide a clear and detailed solution for the following Questions: Question . Let W be…

A: The given subspace W of P3 spanned by S=t3+t2-2t+1, 2t2+2, t3-2t, 2t3+3t2-4t+3. We have to check the…

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

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Q: Calculate the surface integral where S is the portion of the plane lying in the first octant (x ≥ 0,…

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Q: Describe a technique for solving a set of data's numerical derivative. Include the nature of hae…

A: There are several techniques that can be used to numerically compute the derivative of a set of…