Question 4 (a) Solve the following: (b) Explain with the aid of a sketch how this value can be confirmed graphically. Hint: The sketch can be created using computer software or by inserting a photograph of a hand drawing.

Q: Differentiate f(x) = (a-x)(a + x) with respect to x. Assume that a is a positive constant. f'(x) =

A: Solving the problem by finding the value of the differentiation.

Q: Rewrite the following quantities mo 1) e5ln x+4Lny-In z 2) 2Ln√x + 2Lne - 2Lne*

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Q: Given the complex numbers z = 2 + j3,zz = -1 - j2,andzg=4+j4 find; Im (高)x+x@zs)+Im(zz+z) (元)

A: solution

Q: The area bounded by the parabola y² = 4x and the line y = 2x - 4 is equal to {A} 7 sq. units {B} 9…

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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: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

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Q: Find F(s). ℒ{e−8t cos(6t)}

A: To find the laplace transform of the given function.

Q: or values of x which the given the function y=x+1, has a 4.) Find the value maximum or a minimum…

A: You need to find out the critical points then solve for maxima & minima. The explanation part is…

Q: Find the normal line to f(x) = ax² - 4ax at x = 3. Assume that a is a positive constant. Next…

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Q: Use the integral test to determine which of the following diverges. Α.Σ. ke k k=6 1 Β.Γ. Έk? +1 k C.…

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Q: a) yp (t) =) yp (t) = A cos (2t) + B sin(2t) d) y(t) = A cos(t) + B sin(t) Q21) One of the following…

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Q: An engineering firm recently estimated its total revenue function as TR = 300q - 6q2² and its total…

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Q: Show that any subset of bounded set is bounded

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: 1. f(x) = x² − 16x, [3, 10] 2. f(x) = 15 – 2x − 2x², [1, 2] 3. f(x) = 2x³ + 3x² − 12x + 24, [−4, 0]

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Q: Part C- How much would that cost be? Include the dollar sign and no spaces.

A: prices for bowling alleys of bowler world are:-           price to rent shoes   =$5.00…

Q: Find the centroid x of the plane region y=9-x^2 bounded by the positive x and y axes. O x = 3/4 O…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: Use the Laplace transform to solve the given initial-value problem. y'' − 4y' + 4y = t,    y(0) =…

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Q: X 2 1 a X 2 dx

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Q: Differentiate the function with respect to the independent variable. f(x)=-7x+5x³-6 f(x) =

A: Given, f(x)=-7x4+5x3-6

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 16 dx +8

A: We have to find the integral

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: 1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a…

A: You must have an idea about to how to find relative maximum or minimum using critical points.

Q: Given the function f(x)= = Find the difference quotient Find f'(x) by determining lim f(x +h)-f(x) h…

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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: Question 9 Evaluate: lim1 (3-2x)tan (37) O e O None of the choices 01 e 3r O ∞

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Q: * Define this property L (f(t)eat) = F(s-a) Second shifting property O Linearity property O…

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Q: 1) e5Ln x+4Lny-Ln z 2) 2Ln√x + 2Lnez - 2Lne* Rewrite the following quantities

A: Given :1. e5Lnx+4Lny-Lnz2. 2Lnx+2Lnex-2Lnex

Q: Find example where of is continuous and an - bijective but f¹ is not

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Q: ſª √√√x – 1 dx is equal to 8 {A}-- 15 32 {B} - 15 - {c} {D} 8 15 32 15

A: To find out the integration.

Q: Researchers fit data from over 6000 fetal ultrasounds. They measured the femur length, L, (in…

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Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

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Q: € +h (1 g+ dy S

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Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x + 4 and x - 2y + 4…

A: Given problem:- Calculate the volume of solid of revolution when the region bounded by y = √(x + 4)…

Q: Find F(s). ℒ{t3e−4t}

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Q: 1) The hyperbolas 6² x ² - a²y² = a) xyy" + x(y²) ²³²- yy²=0 b) xyy" - x (y² 7² - y₁² = c) xyy" - x…

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Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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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: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the…

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Q: Write the first five terms of the sequence: {√n² + 2n = n}=1 Determine whether the sequence…

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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: (2x-1) dx 1 2x²³²-x²-27x +36

A: …

Q: S dy ² + 4y+20) ²

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Q: () without a calculator. We will do the followings: (1)- 1.2.3.4 7.6.5.4 1.2.3.4 I will introduce a…

A: Using definition of combination

Q: f(t) to f' (t) Option 2 O F (s) to f(t) * Laplace Transform transforms a function from f(t) to F (s)…

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Q: Q22) The inverse Laplace transform of H(s) : = a) f(t) ==e¹+¹e²t 8 8 -3 c) f(t) == est +²e-2t 8 8 1…

A: To find the inverse laplace transform of givem function.

Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

Q: Using the definition, find the derivative of function 2z-i 1 (z)= at the point z = = -¡. z + 2i

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Q: If you apply the limit comparison test to assess convergence 1 - to which of these series would you…

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