Evaluate the following limits. If needed, enter oo for oo and -oo for -0. (a) lim (38z2 – 38z³) = I+ 00 (b) lim z - 00 (38z² – 38z*) = %3D

Q: define the region bounded by y = 0, y = 4√x, y = 24 − 2x, and y = x − 4 using vertical and…

A: Given curves are y=0, y=4x, y=24-2x and y=x-4. We have to define the region bounded by the given…

Q: Exercise 5 a) Given the differential equation y' + 3y = 0,9x. %3D Find A and B so that y = Ax+B is a…

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Q: 4. Consider the function f (x) = 2x + 1. Find the equation of the tangent to dhe %3D graph of f(x)…

A: The given function is                                      f(x)=2x2+1

Q: Find the direction in which f(x,y) = x²e-2y increases and decreases most rapidly at Po(1,0) and find…

A: This is a multivariable calculus problem.

Q: Let f(t) be a furnction on (0, 00) The Laplace transform of f is the function F defined by the…

A: Introduction: In control system engineering, the Laplace transformation is crucial. Laplace…

Q: (b.) Consider the ordinary differential equation in (t > 0) ty" – (t+1)y' + y =0 Note that Y1(t) =…

A: The given ordinary differential equation is ty''-(t+1)y'+y=0...................(1) Write…

Q: Let T:P, →02 be the function defined by the formula T (p(x))=(p(0),p(1)). Then T- (3,5)= (а) 3—2х…

A: Here given T:P1→R2  be a function defind by the formula T(p(x))=(p(0),p(1)). We have to find…

Q: 2222 (mod 13) is equal to O 1 (mod 13) O 12 (mod 13) O 2 (mod 13) None of the mentioned O 6 (mod 13)

A: Properties of modulo function  a≡b(mod n ) then an≡ bn(mod n) a≡b(mod n ) then ac≡ bc(mod n)…

Q: For the function { 0 <t < 3 f(t) = (e2 – 3)? t 2 3 use the definition of the Laplace transform to…

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Q: ||r'(t) × r"(t)|| Use the formula k(t) = to find k(t). |3D r(t) = 4 cos(7t)i + 4 sin(7t)j + 3tk K(t)…

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Q: A function is defined on R2 as f(x,y) = 2x3 – 6xy + 2xy2 +2. Find any critical / stationary points…

A: Given function  f(x,y)=2x3-6xy+2xy2+2 …………………………(1)  Part-a) i)    Differentiating partially…

Q: 30) Find all poin ts (if eny) at honzendal and Verticel fongancy :::: to tul unne Anyw ans: a)…

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Q: In a class of 50 students, 20 are math majors, 35 are computer science majors, and 12 are majors in…

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Q: O If and exist in a neighborhod of (a, b) and are continuous at (a, b) then f(x, y) is…

A: This is a problem of multivariable calculus.

Q: Wk 20 O kle @ clte aoing to put $2500 into that eains t rest On account a Tate Of 12%-1¢ w? to have…

A: Using compund interest formula and continuos compound interest formula.let us solve the problem.

Q: Solve the initial value problem. dy =x*(y-2), y(0) = 9 dx The solution is (Type an implicit…

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Q: ind a function whose tangent lines all form triangles with the xy-axis that are of the same area,…

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Q: S dr 3r+5 r3-8

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Q: Use Green's Theorem to evaluate the line integral. (x – 2y) dx + (x + y) dy C: boundary of the…

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Q: Prove that the necessary conditionm for integrability of the total dif j equation X · dr = Pdx + Qdy…

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Q: J, (5x)cos( 1.5 15 Jk + (5x – 15)cos(- dx 1.5

A: We will solve the above integration as two parts. let f(x) = (5x) cos (nπx1.5)     and     g(x) =…

Q: how that in D4 is not a normal subgroup. Please explain in details and show all the works.

A: To Show, a subgroup in D4 is not normal.

Q: Determine whether the equation is exact. If it is then solvė it oy-7 In y 3)dt= 0 Select the cortect…

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Q: Use cylindrical coordinates. Evaluate Vx2 + y2 dv, where E is the region that lies inside the…

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Q: Determine all minors and cofactors of [6 3 A = 1 -8 -2 1

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Q: o He are going to invest $100,000 in account that Pains 7.5% 00000 at निगाननी interest for 4 S4…

A: Let us solve the compound interest  problem in the next steps.

Q: Find the eigenvalues A1 < A2 and associated orthonormal eigenvectors of the symmetric matrix [3 0 1…

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Q: Find the transform of the ff: a. by calculations b. by using table 1 1.f (t) = 5 sin 4t 2. f (t) =…

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Q: a. The price of a jumper was reduced in a sale by . The new price was later reduced by . What…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 2 3 4 5 6 7 2 7 1 5 3 1

A: Here given permutation as 12345676271534

Q: Which of the following products of trigonometric functions of different frequencies is equivalent to…

A: This is a problem of identity and counting and frequencies.

Q: Let L = (a" : n2 0}. Which of the following is true? O a. L = L but Lt # L. O b. L' # L but L* = L..…

A: This is a question of Automata theory.

Q: Find the general solution of the given variable sopardble eguation. ) dy 3x²+4y² %3D

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Q: Consider the function x - 3 for x4 By using the characterization of continuous function in terms of…

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Q: Let A be a 6xó matrix with the characteristic equation 1?(1 - 7)(A - 12)3 What are the possible…

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Q: Study the patterns of numbers in each row of the table below. Each row relates to one of the figures…

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Q: 2. Suppose that f(x) = { ( 1 if – 2 < x < 0, 2x if 0 < x < 2. Let s(x) be the Fourier series for…

A: f(x) has jump discontinuity at x=0, x=-2 and x=2 . The Fourier series converges to the average value…

Q: Response 2: Write an augmented matrix based on the results from Response 1. Solve the matrix. You…

A: Solution

Q: f (1, 2) = 3 and the function f (1, 2) in the direction of i + j is given as 0.7. Using this…

A: Given that f1,2=3 and the derivative of function f1,2 in the direction of i+j is given as 0.7. We…

Q: 1. Let l: R2 → R³, l : x+ Ax, where k k %3D 2k –1 9 a.) Establish for which value of k, the linear…

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Q: 25 s3(s? + 4s + 5)

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Q: S() = {2 -1st<0 0st<1 f(t + 2) = f(t) for alle t.

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

A: To find the domain of r(t) and the value of r(t0).

Q: paper 2 4. INDICES AND SURL 2019 N FUNCTIONS + INDICES AND SURDS Q2 Do not use a calculator in this…

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Q: 22

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Q: Show that the equation dy + 2k possesses solutions of the form 00 - kt E c,e cos (oa,x+ E,) cos (w,…

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Q: Q5) Find the integration by using (by part method): Se3x sin X dX

A: We can solve this using part method

Q: 1. Trigonometric function fre)= -3 +4 cos(rt-) TT 9? what is the Max and min values att ained by…

A: Introduction: In trigonometry, the sine function is one of three primary functions, the others being…

Q: 3. (x³-x²)7 dx x2

A: As per the question we are given a indefinite integral, which we have to find out. And to do that we…

Q: Four legged animals Tun with two types of motion:trotting and galloping.An animal that is trotting…

A: For a function: y=f(x), the dependent variable is y and the independent variable is x. The value of…