Find an eigenbasis and diagonalize. (Show the details.) 101 72 9. -144 -103.

Q: The integral of the given function ſ 3(x-1) dx is equal to (3x+1)ž

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Q: Question 3 - a) ji following series : Determine whether the (-1)"4"-1 32n+1n n=1 is convergent or…

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Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

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Q: L, V4 – x²dx.

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Q: ( d ) Σ0, 3i (i2 + 2) i=1 3i(i² + 2)

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Q: O Question 17 Evaluate the integral dx (7x2 + 1) by making the appropriate substitution: dx = (7x2 +…

A: Solving

Q: The period of y = 2 sin 4x is _____. 2 pi/2 4pi

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Q: d'y (3x* – 5)(2.x² +9x–6) Determine the of y = 3 dx 7x

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Q: Find the derivatiives of the following functions using DELTA METHOD. 1. f(x) = 3x – 2 2. f(x) = (3x…

A: We know that f'(x) = lim∆x→0fx+∆x - fx∆x

Q: a) Determine whether the series (-1)"n² 00 Σ is convergent, n3 + 3n + 1 n=1 absolutely convergent or…

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Q: What are intervals of concavity of the function f(x) = 2x - 6x² – 3 ? Concave upward on (1, o) and…

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Q: The polar coordinates of a point are given. Plot the point. (4, 7/2) y y 10 10 5 (4, 7/2) (4, 7/2) X…

A: Given polar coordinate is (4 , π/2) We have to find the rectangular co-ordinates.

Q: 44 3) y" +y = sec?x (Use variation of parameter method)

A: To solve the given differential equation.

Q: 7. Su° (4 + u°)°du

A: The objective of the question is evaluate the indefinite integral.

Q: Compute the following limits: cos (x) (i) lim x3 tan(3x) (ii) lim

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Q: x2 +y? +z? - 4x + 8y – 2z = - 12

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Q: 3. V4- (x – 3)²dx.

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Q: n²+4 2(-1)n-1 2 n=1 n²+ 3

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Q: Find the sum of the first 7 terms of the following series, to the nearest integer. 6, 12/5, 24/25,

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Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

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Q: For the points P1 (4,2,3) and P2(5,1,2), find the direction of P,P2 and the midpoint of line segment…

A: Given that coordinate of point P1 is (4,2,3) The coordinate of point P2 (5,1,2) We have to found the…

Q: Spot the source/start of the mistakes and say something about it. S2 sec (a) dæ Given: Step 1:…

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Q: e3 1 - Find lim

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4: A- Solve the differential equation subjected to the condition y0)=1 dx

A: Firstly separate the variables and integrate on both sides and solve the differential equation.…

Q: 4x + 6 2x2 + 5х + 3 X-1 2х + 4 6. %3D X+ 2

A: According to guidelines, we can answer only one of the multiple questions given. Submit the…

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: Consider the function f(x) = x2 -1 %3D (a) Find the intercepts of the graph of f (if any). (b) Find…

A: The given function is: f(x)=xx2-1

Q: 3. Evaluate: lim X-0 \sinx 4. Using the binomial series, find the power series of f(x) =

A: We have to find the limit of a function and find the expansion of 1/x

Q: Evaluate the following limits: (1) lim (V +1- V). x→+∞ |2² – 1| (z^ – 1+8^) (ii) lim x-1 x – 1 x<1

A: Limits

Q: From the textbook: Let f be the function in the graph below. (1) Going from left to right, this…

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Q: Use the definition of continuity to show that h(x) = x^2 + 5x/2x + 1 is continuous at the number a…

A: The given function,   h(x)=x2+5x2x+1

Q: Q: Solve the following D.Eqs. (Use undetermined coefficient method) 1) y" – 2y' + y = xe* 2) y(4) –…

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Q: 1- sin r 6. Find lim 1/2 CSC x Csc x

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Q: Give an example of a differential equation  and  classify according to   order, degree ,linearity…

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Q: -3 1 4 What is the transpose of the matrix 5 2-1

A: Transpose of a matrix can be found by interchanging the rows into columns or columns into rows.

Q: P= 8,6)

A: Given vector v=5i+3j+4k  The point p is (6,8,6) and we called P is Position vector.

Q: The function f: R R defined by f(x) = cos(r-) is O a. onto but not one-to-one. O b. neither…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 12 –…

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Q: S(x² – 1) Vx + 4 dx 4.

A: 4.∫x2-1x+4dx

Q: Express the following sums using sigma notation. c. 12 + 22 + 32 + 4² 4 c. 12 + 22 + 32 + 4? = E k=…

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Q: 12. Find the inverse Laplace: Lª 1 |(s- 4)ª [* et А. e443 В. e44 e43 D. 6 C. E. None 24

A: Inverse Laplace transform shifting property:

Q: Assume that the radius r of a sphere is expanding at a rate of 80 cm/min. The volume of a sphere is…

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Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k…

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Q: Find the general form of f if f'(x) = - 5f(x). f(x) =

A: Given that,      f'x=-5fx

Q: 2n +3 an %D 5n+8 hen the series an n =1 is divergent Select one:

A: Given query is to find series converges or diverges.

Q: dy da = y+ Vx² – y? O y = x cos(ln|æ|+ C) O y = x sin(n|x| + C) sin-1 (를)-In|미=C coS-1 (2) -Inl피 =C

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Q: Give the range of the function f(x) = -x 2. all reals y ≤ 0 y ≥ 0

A: The given function is: f(x)=-x2

Q: Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder.…

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Q: 422+8z-18 dz 3. S

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Q: If T is the point at the given distance on the unit circle C from P (1, 0), determine the quadrant…

A: Here, T is on the unit circle, and its distance from the point P(1,0) is 13π12 that is: