Prove the following, using the definition of a limit (convergence to a point). 3 n+2 lim 2- 004-u = 2.

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A: The given function fx=x2+3x over the interval 0,8 with x0=0, x1=1, x2=3, x3=7 and x4=8 Riemann sum:…

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Q: 3 If ƒ (x) = 2 + x, evaluate Σƒ (k+1). k=1

A: We can answer the question as below.

Q: Use the matrices below to perform matrix multiplication. B If the operation is undefined, enter NA.…

A: Please see the below picture for detailed solution.

Q: 7/2012 - y x² + y² (²) di dx + (ye³ +2²) dy = 0

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Q: Consider the region R bounded by the functions f(x) = 3x and g(x) a. (4,2) b. (4,1) c. (22², ²) C.…

A: Region R is bounded by the functions f(x)=3x, g(x)=x2+2 Their intersection points…

Q: 6. Which of the following expresses (3√32 + √√8 ) in simplest form ? a) 3√40 b) 6√10 c) 3√2 d) 14√2

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Q: 5. Find the functions whose equations in factored form have a factor that is squared. These…

A: Here is a structure of a function whose equation in factored form has a factor that is squared:…

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Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

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Q: For the function y = f(x) = 3x³ – 10: df dx a. Find ƒ'( − 2) b. Find a formula for x = f-1(y).…

A: NOTE- "Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: 10. Given two vectors u = [6,2] and v=[-2,1], determine the projection of u on v.

A: #10

Q: Which one of these is a vector equation for a line in 2-space? y = 3x + 7 =(-2, 1,0) + s(-4, 2, 1) +…

A: Given ○y=3x+7○r→=-2, 1, 0+s-4, 2, 1+t1, -1, 2 s,t∈R○3x+4y+7=0○r→=2, 1+t-1, 3 t∈R

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Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) -3 lim x-4-(x-4)²

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Q: -5 -4 -3 -2 -1 5 4 3+ 2+ 1+ -2- -3+ -4 -5+ ܐ 2 3 4 5

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Q: 70. S tan-1 x dx 1+x²

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Q: 8. Simplify 2√80-7√20 a) — 6√5 b) 90 c) 5√22 d) 22√5

A: Concept: Square root: The symbol for a number's square root is n. The outcome of multiplying or…

Q: 1 and g(x)=x² +2, then go fmay be expressed as x-2 axa + 2ßx + ¥ χα + βχ - β If f(x)=- g(f(x)) = =…

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Q: What is the integrating factor of the differential equation (5xy + 4y² + 1) dx + (x² + 2xy) dy = 0?…

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Q: 9. Given vectors = [3,-6,8] and v= [4,-2,-5], determine uxv.

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Q: Given the following function, find the values of f (5,2) x = 5 + xln(xy-9) f(x,y) O A. 25 OB. 10 OC.…

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Q: 14. 2y dx + x(x² In y − 1) dy = 0. -

A: To find the solution of the given differential equation.

Q: Consider the function given below. f(x) = sin 0, 1 X+1 1 x < -1 x≥-1 Complete parts (a) through (c).…

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Q: Σ(-1)^+¹ Test k=1 1 for absolute/conditional convergence

A: The given series: ∑k=1∞-1k+11k5 .We need to test for absolute onvergence and conditional…

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Q: Calculate r' (t) and T(t), where T'(t) = ( T(t) = { r(t) = (8+t, (9+t), 2+2t). ).

A: Given vector function r(t)=8+t, -9-t, 2+2t

Q: 225 ft ☐☐ X A building that is 225 feet tall casts a shadow of various lengths as the day goes by.…

A: Topic- Application of derivatives

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Q: 15 Lo - - dx 15 X (x + 1) ²/ O 0 O or| 800 88 O 1 O 176 5

A: The answer is 0.

Q: The infinite series Στη O series liner O p-series O geometric series O harmonic series n is a

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Q: Use the graph of the function to estimate the local maximum and the local minimum of the function.…

A: We have to use the graph of the function to estimate the local maximum and the local minimum of the…

Q: Find the equation of the tangent line to f(x) = 4x² -5x+2 at (-1,11).

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Q: Evaluate I se sech¹0d0. 4

A: We have to find out integral

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Q: 5-4-3 2-1 10 9 8 7 6 5 1 y 4 32 3+ 2+ 1 2 234 3 4 5 -6 1 2 3 4 5 X

A: Please see the below picture for detailed solution.

Q: im not really understanding because its typed

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Q: Question 5 (i) Use the diagram below to find sin(0), cos(0) and tan(0). (ii) If sin (500) -1…

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Q: f(x) ax² + B where x denotes the length of one side. Find a + ß. Your answer

A: We have given  fx=αx2+βx Put x=1 in fx f1=α12+β1 f1=α+β So, α+β=f1

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Given that f(x)= e3x (8-x) . We find intercept point and relative maxima and minima and point of…

Q: If -y³ − 3 − x³ + 2y – 2y² = 0 then find dx in terms of x and y.

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Q: A company that produces cell phones has a cost function of C-52²-1852 +17363, where is the cost in…

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Q: Question 7 (1 point) ✓ Saved The point (1, 2, 4) is on the line 2+³ = 1+4 = 25 True False

A: We have given equation of the line x+35=y+44=z+53 Put x=1,y=2,z=4 1+35=45 Similarly, 2+44=64=32…

Q: The following table shows the rate of water flow (in L/min) through a dam. 1 5 9 13 17 21 25 t (min)…

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