In the diagram, AABC is an equilateral triangle, and D, E and F are the midpoints of its sides.

Q: J (secs x) dx/csc x

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Q: A car drives 30 km northeast, then 10 km south. Its displacement from its original position is a)…

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Q: If X(z) is the z-transform of the signal x(n), then what is the z- ?transform of the signal x(-n) x…

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Q: Q2) Determine using Cauchy Riemann equations the function below is analytic or not? f(2)=x² +…

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Q: *.The equation (y"+x3y'+y=sinx)is.............. differential equation Linear,2nd order, Homogenous O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Consider the following. y = = In(x²) Find y'. y' = Find the slope m of the tangent line to the graph…

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Q: Show that: le a (i) a е a а al (2a +1)(1-a)2

A: Given :laaalaaal=2a+ll-a2

Q: ל 15 18 a = (3₂16) 6= (-2,0,1) → 08 -> 2² = ²²-23 +5k →> oc CẢ OA

A: Given :a→=3,1,6=OA→b→=-2,0,1=OB→c→=i-2j+5k=1,-2,5=OC→

Q: 2. A 6-ft tall man is walking away from a 15-ft post at a rate of 5 ft/sec in a straight line. How…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Show that: l (i) a a a a al la al = = (2a +l)(l

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Q: A transportation company sells 2000 bus tickets per day when the price is $10 per ticket. They…

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Q: Given: y = = 4 cot (3 - 2x) Find: dy dx 0-8 csc² (32x) O csc² (3-2x) 08 csc² (3-2x) -4 csc² (3-2x)

A: Given y=4cot(3-2x)To find dydx:

Q: -4x 2. Determine an equation for the tangent to the curve y = (x+3)² at x = -2.

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Q: Q3) Given, u (x, y) = xy is harmonic, find a harmonic conjugate v(x, y), write u+iv as a function of…

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Q: 3) (11x + 17) dx 2x² + 7x - 4 S

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Q: Find the number in the interval [0,3] such that the difference of its square from its cube is the…

A: Given problem:- Find the number in the interval [0, 2/3] such that the difference of its square from…

Q: Let ā (3, 5, - 4) and 6 = (1, 4, 3). (à − b ) × ( ã + b) =

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Q: Determine two numbers whose sum is 36 and whose product is the largest possible. 20 and 16 15 and 21…

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Q: 1. dx/(x - 1)³ 2. (1-x²)² dx 3. f (x² - 1) x dx

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Q: A drink can, in the form of a cylinder, needs to have a volume of 750 cm³. The material for the top…

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Q: dx f(x2²x+10) ² २

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Q: Find the final value of the system corresponding to

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Q: Find the average value of the function f over the interval [0, 15]. 4 f(x) = x + 1

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Q: 12. Setan 2x sec² 2x dx

A: As per guidelines we can solve only one questions at a time, so if you need more answers kindly…

Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: c) What is the loss the company incurs when it tries to maximize sales (that is, produce the maximum…

A: Find out the loss the company when it tries to maximize the sales.

Q: c) y(x) = c₂x² + ₂x Q20) The form of a particular solution of y"-4y' - 12y = sin(2t), is: . a) y,…

A: Using inverse operator

Q: Investigate if the integral dx 1-x is convergent or not. Justify your answer.

A: Divergent

Q: 9. f (cosx-sin x)² dx

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Q: Find the rate of change of the volume (V) of a sphere with respect to its radius (r) when r = 4. 4π…

A: You must have idea about basics of derivatives. The rate of anything is basically the derivative…

Q: Evaluate: S O (1+2√√)¹ 2 O (1+2√)¹ +C 8 O 2(1+2√x) + C O (1+2√)¹ - + C 4 (1+2√x)³ - dx +C

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Q: Find the area of the surface generated when the given arc is revolved about the y-axis ㄷ y = 4 - x²…

A: We have to find area of the surface .

Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: a) e b) e-t Q24) The Integrating factor which make (3x2y + 2xy + y³)dx + (x² + y²)dy = 0 exact, 15.…

A: A detailed solution is given below.

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 8 sin(t). The initial…

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Q: f(x) = = 250 x1.40

A: As we know that; The Power Law: ddxxn=nxn-1 And a·f'=a·f', where a is constant.   The given function…

Q: Find the derivative of the following exponential and trigonometric functions: please attach your…

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Q: If [ f(x) dx = 12. g(x) dx = -2 and L₁ dr following gives the value of [[1²)+ 4 76 Sh +4g(x)- h(x)…

A: Given:     ∫-36fxdx=12     ∫-36gxdx=-2     ∫-36hxdx=-7

Q: Suppose f(-1) = 1, f'(-1) = 5, and g(x) = x³ f(x). The tangent line to g(x) at x = 1 is given by y =

A: The objective is to find the equation of tangent line .

Q: Which of the following definite integrals setup (in terms of y) provides the area of the region…

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Q: Which of these series, if either, converges absolutely? 00 1 1 1.Σ(-1)* 1.Σ(-1)* 1 k=1 k=1 k+ k² +…

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Q: integrate [(x csc^2 (2x) - x cos (2x)] dx

A: Given problem:-  ∫ [(x csc2(2x) - xcos(2x)] dx

Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

A: We have to prove the given equation of complex number

Q: Question 3 limx→+∞ e-√√ OI Oll O III OIV O Not Indeterminate

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Q: Find f'(x): f(x) = sin(2x) O 4sin (2a) (2 ln 4) cos(2x) O 4sin (2x) (2 cos(2x)) O 4sin (2x) (In 2)…

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Q: lim-0 OI Oll O III OIV e² - x Not Indeterminate کے

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Q: 20 e dx x Inx

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Q: 6 sinh t 6 cosh 51 Option 2 O Option 3 * What is inverse Laplace for 6s s² +25 6 sint 6 cos 5t…

A: In this question, we need to find the inverse Laplace of given function.

Q: 4x* dx

A: We need to solve the following. So,            ∫-224x4dx=4·∫-22x4dx=4x55-22=4·645=2565

Q: X 2 1 a X 2 dx

A: