Determine the 2.x2 – 4x + 6 dx using the definition. (hint: lim Rn)

Q: no 2n? -5 sin( n) d] lim %3D 3. Prove or provide a counterexample for the follow

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Q: Let a be a nonzero constant such that a + 55. Let ax? + sin? y 55x² + y² f(x, y) = and let L =…

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Q: Q2/ a) If f) = , what are the domain of f(x) and g(x)? sin 6x lim 0 sin 9x b) Find

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Q: Evaluate using Theorem as necessary.

A: Given limit: limt→0 t3+9sin tt We can write the above limit as limt→0 t3+9sin tt=limt→0 t3+9×limt→0…

Q: Calculate lim r(t), where r(t) = (r², 1 – 1,171).

A: rt=t2, 1-t, t-1

Q: Choose the correct answer for the following limit S sin t3 dt lim 3x4 (A) (8) -1 (C) 1 4 (D) 4. (E)…

A: Let us consider the function F(x)=∫a(x)b(x) g(t) dt Then the derivative of the function is given by…

Q: Find the 2x -3 lim 4x +1 DNE O 1/2 2. What is the

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Q: Which of the following corresponds to the x-4 √x-2 evaluated? 0 4 2 DNE limx→4 ( when

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Q: of e dydx

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Q: Which of the following expres zy 0 = .lim(z,9)¬(0,0) F+ y²

A: Let us substitute: y = mx Then we get, Limit as (x, y) tends to (0, 0), [(xy)/(x2 + y2)] = Limit as…

Q: Q3/ By using definition, proof that cot x = - csc? x. dx %3D

A: In this question we will use basic of calculus i.e concept of differentability. Solution of the…

Q: Determine whether the following statements is true or false, and explain why.

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Q: Use symmetry to evaluate the followingintegrals.

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Q: For B = – lim r² -1 6 sin z which one is B?

A: In this question we have the limit for B.

Q: - Complete the following statement. (x? + 3) dx = lim where Ax = and x; is

A: To complete the statement

Q: So sin(t²) =? lim, »0* O a. Limit does not exist O b. 1/3 O c. 00 O d. 0 O e. 2/3

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Q: 7 Calculate 2x+ x-) dx, given the following. 7 8 218 169 Xdx xdx = 12 3 3 7

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Q: 8r + 5tant Find lim t>0 sint

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Q: Please

A: To find:

Q: Use symmetry to evaluate the followingintegrals.

A: Given:∫-11 1-x dxIf f is an odd function f-x=-fx∫-aa fx dx=0If f is an even function f-x=fx∫-aafx…

Q: b. b-a Use the equation fte)dx = lim ** ) to evaluate the following definite integral. n-0k=1 2 |(2x…

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Q: 1. Use a substitution to find (6x2 2)e*+¤ dx showing working.

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Q: 2y-n -Tt 7. lim cos y 2

A: Given:         limy→12π2y-πcos y    Let   π2-x=y, ⇒π-2x=2y      As y→π2,x→0

Q: Determine the value of c for which 42 8n lim (1+ n00 cn

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Q: 42. (a) By completing the square, show that 1/2 dx T x² – x + 1 3/3

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Q: Evaluate the limit. sin? 3t lim t-0 O DNE O 0/0 O 3 9,

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Q: Let a be a constant. Given that -107 3x In(ax)dx = el8 ( 42 – 3. find In a. 3 %3D

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Q: Find the limit. j+ tan(2t) k sin?(t) -3t i + lim t→0 e

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Q: Use symmetry to evaluate the followingintegrals.

A: The given integral is ∫-22x9-3x5+2x2-10dx.

Q: After appropriate substitution, the integral expression a* (x2 + 4)? dx can be express as (choose 2…

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Q: Find values of a and b for which cos (ax) – b -1. lim x→0 2x2

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Q: sec2 X dx 3

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Q: Use n = 6 subdivisions to approximate the value of Vx +2 dx by the trapezoidal rule.

A: The given integral is ∫06x+2dx and the value of n is 6. Using the trapezoidal rule, approximate the…

Q: )find dy to yalog,o(3X+1)

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Q: Which of the following is not correct? 4dx 4dx A Jo Jx(x+6) = lim o Vx(x+6) C+ .3 dx .3 dx B h…

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Q: dx 7. S; x³ Vx2-4

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Q: 4. 4. f_x²dxdx (9-x²)

A: The integral is given as ∫x29-x232dx. We have to evaluate the integral using trigonometric…

Q: t+1 e i+ sin 2t lim 花1=?

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Q: is Substitute for +4 X = 2tano and dx= 2 Secodo %3D

A: Given integral is ∫x3x2+4dx Substitute for x=2tanθdx=2sec2θdθ

Q: lifferen tiake 3-Co5hx with respect to X 6+ sisht

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Q: ) Find the derivetine of the fnchiog h(x) = I sinhex-7x 4

A: h(x)=74sinh(2x)-7x2Differentiate w.r.t…

Q: dx 2 x + : P14 25.

A: Find the value of the integral.

Q: Which of the following imits is equal to a dx? 3. 72 1 lim 3+ k=1 2. B lim 3+ - k=1 2k 3 + 1 C lim…

A: We have to find

Q: D Find lim X,Y)→ (5,1) XY X+y or show it DNE.

A: We have to find limit

Q: B) f(x) = x+3 (-6, 6<x<1 Is f cont. at x-6?

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Q: lim-sin t t0 In(2et_1) %3D A © D B.

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Q: Find Jog %3D 1-cosx dz n=770

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Q: Find the convolution of fix) = sin bx, g(x) = exp(-alx), a>0.

A: Convolution: Let and be two piecewise functions, then the convolution of them is denoted and defined…