Use L'Hospital's Rule to evaluate the following limits. ex-1 a) lim (x²-x³)e²x b) lim X118 x−0 tanx c) lim_(tan x) cos x X→(π/2)-

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

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Q: If A 0 " P= [13] AP= PA, then what is A¹⁰ ?

A: Given: A=5-230, P=1213 To find: A10.

Q: 1 a 1 b C f(a) (x-a) 1 f(b) (x-b) f(c) (x-c)| a² bb² a с f(x) (x-a)(x-b)(x-c)

A: we expand the left side determinants.

Q: So So √√₁-x² √1-x²-y²³ (1 + x² + y²) dzdydx 0

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

A: We have to show that any sequence of positive real numbers either has a subsequence that converges,…

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A: The given series, 1. ∑n=1∞4n+2n3n 2. ∑n=1∞sinn3 3. ∑n=1∞1n2+2n 4. ∑n=1∞n+2-n. We have to check the…

Q: ! 0. JUUTTUU M 10. Compute the distance between the functions f(x) = 5 + x and g(x) = 6 + 3x in…

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Q: For each of 17-24, choose from among: a) f(x) is O(g(x)) b) g(x) is O(f(x)) c) both of the above d)…

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Q: binomial theorem to expand (a2 _ 3)4 . Show your work.

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Q: WORK PROBLEMS (6 Question 1 a) i b) c) s): You must provide a clear and detailed solution for each…

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Q: 1. The following subsets A, B, and C of R XR are relations on R. Sketch the set. (i) B = {(x, y):…

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Q: Find the area of the shaded region. Enter your answer as a reduced fraction. -3 A = (-2,3) (-2,-1)…

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Q: Question 2 ( a) Evaluate L{eot} b) Evaluate C{(t−2)² + sin 6t + cos 7t} c) Use the Laplace transform…

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Q: Suppose that B is the matrix obtained from A by exchanging row i and row j of A. Prove that det(B) =…

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

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Q: Which of the following is the even periodic extension of the function f(x)=3x⁹-x²+x³-4, 0<x<L with…

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Q: Let A, = is constant. r-1 n (r-1)² 2n² (r−1)² 3n³ 6 4n-2 3n²-3n Show that A, ΣΔ, r=1

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Q: Sketch the graph of the following function. Identify the domain and range. f(x)=√x - 2 Domain:…

A: We have to solve given Questions.

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

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Q: Ifx +2y+32 = x2 + 2y2 + 3z2 = x² + 2y3 + 3z3 = 2, and xx +2y2y3 +3z₂Z3 = x3x₁ +2y3v₁ +3Z3Z1 = x₁x₂ +…

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Q: The volume of the solid bounded below by the xy-plane, on the sides by p=4, and above by p=- -5,0 is

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Q: If a₁, 92, 93, determinant: ... are in A.P., then find the value of the following ap+ap+m+ap+2m…

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Q: Match the formula of the logarithmic function to its graph. Graphs of Logarithmic Functions 4 v Q…

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Q: Set up a double integral to represent the area of region D, the region outside the circle r=3sin and…

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Q: Let A = 15 0 13 2 x = 1 - 12 and b = 3: 15 25 73 Define the linear transformation T: R² → R³ by →…

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Q: Solve y" +2y(y)² = 0 d. a. ²²-₂y=x+₂ - 1 b. y(x)=c₂ex_ c. (C₂-y)² + x² = C₁ y=C₂-In(C₁-x²) d. e.…

A: The given differential equation is  y''+2yy'2=0 Our aim is to find the solution to the differential…

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Q: Which of the following is a subspace of P3 (the set of all polynomials of degree less than or equal…

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Q: a) Find the Fourier series of the following function. 1 x² if π < x < 0 if 0 < x < T 0175 Show…

A: Given: fx=1if -π&lt;x&lt;0x2if 0≤x&lt;π We have to find the Fourier series of the given function.…

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Q: If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) f(b) (x-b) f(c) (x-c) a 1…

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Q: (a) Use a calculator or computer implementation of the Runge-Kutta method to approximate v(t) for…

A: As per the question we are given the following differential equation : dv/dt = f(t,v) = -0.04v - 9.8…

Q: -15 8 -7 2 8 -5 -1 1 Determine the four eigenvalues of A. ● Determine all of the ordinary…

A: Given system x'=Ax = -158-164-72-1058-57-1-11-2-2 x, Part (1):- Determine the four eigenvalues of A.…

Q: Obtain the particular solution. (EXACT EQUATIONS) 3. 3y(x²-1)dx + (x³ + 8y − 3x)dy = 0, when x = 0…

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Q: A certain province widely cultivates maize crops during the dry season. The average weight (in tons)…

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Q: If x² +2y+3z? = x² + 2y² + 3z² = x² + 2y3 +3z3 =2, and x₂x3 +2y₂y3 +3z₂z3 = x3X₁ + 2y3V₁ +3Z3Z1 =…

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Q: 3. 2. {2C} Find the domain: Goo, {2F} Find where the function is increasing: -7,00) {2F} Find where…

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Q: Let S be a linear transformation from R³ to R² with associated matrix A = - 2 0 -1 2 2 1 2 Let T be…

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Q: For the production of tables and chairs, the furniture factory uses three type of wood. Cost rate…

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Q: ²₂² √²/² x dzdxdy So 4-x² 4-x²-y² -2 4-x²-y²

A: The given integral is : I=∫-22∫04-x2∫-4-x2-y24-x2-y2xdzdxdyAs z≤4-x2-y2⇒x2+y2+z2≤22Also…

Q: Use the Gram-Schmidt process to produce an orthogonal basis for the column space of matrix A. C A =…

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