14. 2y dx + x(x² In y − 1) dy = 0. -

Q: Suppose that p(t) is the growth rate of a population of bacteria at time t minutes. What does 15…

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Q: 3. A particle moves along the x-axis with velocity v(t) = t2-1, with t measured in seconds and v(t)…

A: Given velocity v(t)=t2-1 To get the total distance traveled, we have to integrate the velocity…

Q: 1. A rectangle has a perimeter of 14 m. Express the area of the rectangle as a function of the…

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Q: Determine the following limit in simplest form. If the limit is infinite, state that the limit does…

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Q: A diabetes test is positive 85% of the time when the patient has diabetes and negative 95% of the…

A: Given data:- Diabetes test is positive 85% of the time when the patient has diabetes  diabetes test…

Q: 3. A ladder 10 feet long is leaning against the wall of a house. The base of the ladder is pulled…

A: Concept: Let x represent the distance from the wall to the ladder's base. and let y be the height of…

Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

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Q: 10 5 f(x) 10 5 10 10 X

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We need to find maxima and minima.

Q: 3 14 f(x) dx where a = 5 - ["² f(x) dx = [ f(x) dx 3 a and b =

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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: 1. (x³ + xy²)y' = y³ Ssangen job10 2. (2x + y)dx= xdy 3. x³y' + x²y-y²= 2x4

A: Topic:- differential equation     Definition:- The order of a differential equation is defined to be…

Q: Consider the function f(x) = 6x¹0+ 3x5 - 2x³ - 3. An antiderivative of f(x) is F(x) A is and n is…

A: The given function fx=6x10+3x5-2x3-3 use the integration formulas, ∫xndx=xn+1n+1+C∫dx=x+C

Q: Question 6 Determine the Fourier series for the function defined below: f(x) = 2x in the range x = 0…

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Q: 5) Calculate the area of the region between the curves: y=2-x² and y=x²

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Q: An internet bookstore charges $15 shipping for orders under $100 but provides free shipping $100 or…

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Q: Express a = the limit lim Σ(4(x*)² – 3(x* )³) Aï; over [6, 7] as an integral. n→∞ i=1 Provide a, b…

A: The given limit limn→∞∑i=1∞4xi*2-3xi*3∆xi over the interval 6,7

Q: 4 sin(x - 2) x→2 3 ln (3x – 5) Evaluate lim and write your answer in simplest form.

A: We can find the limit in the following steps.

Q: Consider the function f(x) = x² + 2x - 8 x - 3 a. Find the first derivative. f'(x) b. List any…

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Q: 19. 2x³y = y(y² + 3x²).

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Q: Evaluate f(1). b) Evaluate f(-1). c) Solve f(x)=2. d) Solve f(x)=-

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Q: X 2 Find x² +1 -dx

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Q: On the line y = 2x + 1, what value of Δy corresponds to Δx = 3? Δy =

A: y=2x+1 We have to find ∆y corresponding to ∆x=3.

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

A: We can answer the question as below.

Q: Let f(x) = x³ + 3x² (a) Use the definition of a derivative or the derivative rules to find f'(x) =…

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Q: Calculate: fx²e³dx

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Q: What is the max area of a rectangle placed between the x-axis and the function f(x)= -x^4 + 3

A: To determine the maximum area of a rectangle placed between the x‐axis and the function fx=-x4+3.

Q: Find the length of the curve r(t) = Interactive 3D Graph (√2t, et, e-t) over the interval 0 ≤ t ≤ 1.…

A: The given curve rt=2t, et, e-t over the interval 0≤t≤1 To find the length of the curve on the given…

Q: 2. Suppose a population of insects grows exponentially, there were 130 insects after the third day…

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Q: -4 -3 -2 -1 -5-4 5 4 3- 2+ 1 -Y -2+ -3+ -4+ -5+ 2 3 4 5 X

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Q: -3 -2 -1 у 1 - 1 -2 -3 -4 -5- 1 2

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Q: Given the function graphed below, evaluate the definite integrals. 4+ 3 2 1 -1 7 -1 -2 -3 -4 1 S.³…

A: Need to find out the definite integrals.

Q: -10-8 6 4 2 2 4 6 8 10 2 4 6 8 10 X

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Q: Consider the rational function f(x) = x²-x-6 x²+3x (i) Factorise the numerator and denominator. (ii)…

A: As per guidelines, we must answer only three of the subparts of a question given. So, I answer the…

Q: 4. Find the area bounded by the curve a²y = x³, the x - axis, and the line x = 2a. Solve in two…

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Q: Wha is the derivative of exp(22²)? ○ 4a exp(2x²) exp(2x²) 2x² - exp(22²) exp(4x) ○ 4x exp(4x) ○…

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Q: Given the function f(x)= |x-1|: (a) explain why f(x)= |x-1| does not have an inverse function over…

A: Given fx=x-1

Q: Explain why the integral is an improper integral and evaluate it: =dx √x-2

A: Given integral:- ∫251x-2dx

Q: 3. 2 csc 2x = sec x csc x

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Q: Given f''(x) = 3x + 3 and f'(-3) Find f'(x)= and find f(2) 1 and f(-3) = 5.

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Q: f(x) = 2 - 1x + 1 4 (x - 4)2, x + 16, x ≤ 0 0 <x

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Q: You have an investment of $22,400.00 that you want to double in 11 years. If interest is compounded…

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Q: If f(x) f'(x) = [ 7-x² 3+x² find:

A: Topic = Derivative

Q: Calculate the length of arc of y = 2x/² for 0≤x≤1

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Q: The angle between two vectors a = (1, 1, 2) and b = (-1, 2, k) is 60°. Find the value(s) of

A: Topic:- application of vector algebra

Q: Find the value of C so that y(t) = Ce2t satisfies the initial condition y(1)=1

A: Substitute t=1

Q: 4. Find the range of the function F(x)=√36-t² dt O [0, 36π] O [0, 18π] O [-6, 6] O [-6, 0]

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Q: Find the area under the curve y=sin2xcosx for the given limits; sketch the area. Hint: integral in a…

A: Topic:- application of integration

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: Answer the following True or False: If f(x) is a differentiable function such that f'(-4) = 0, then…

A: Given that the function f(x) is differentiable function and f'-4=0 We need to verify whether its…