Consider the region R bounded by the functions f(x) 3x and g(x) = x² + 2. The ar a. 2 sq. units b. 3 sq. units c. sq. units d. sq. units 6 =

Q: Question 2 Determine the solution of the second-order differential equation: d²y dx 2 dy -7—+12y=e²³…

A: Ode

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Q: -3 -2 -1 у 1 - 1 -2 -3 -4 -5- 1 2

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Q: kmarks Window Help 0 -7- The graph of f(x) is given below. Which of the three conditions for…

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A: Given  f(x) = -5-x2+2if  x≠-62x+14if  x=-6

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given in the figure A1 = 7 , A2 = 3,  A3 = 2  and A4 = 2. Concept:-  If In [a,b] y = f(x) ≥ 0 then…

Q: 8. Find the equation of the exponential function g(x). (No Decimals) Equation: -6 a

A: Solution ) from the graph  ( 0 , - 2) and ( 1 , 2 ) points are on the graph  Equation of exponential…

Q: 1. Determine the equivalent ODE by eliminating arbitrary constants y = ae-2x + bxe-2x Oy" +4y' + y =…

A: Given data:- y=ae-2x+bxe-2x

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Q: √= - 4x + 43 x² 11x + 18 dx = +C

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Q: Which of the following represents a possible equation for a sinusoidal function with an amplitude of…

A: answer is in next step. please give a like!!

Q: Consider y=√x+1. (a) Find its inverse relation. Is this relation a function? Why? If the inverse is…

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Q: 13. A radioactive isotope has half-life of 43 days. What percent of the original amount remains…

A: Topic:- application of algebra

Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

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Q: A fast-food restaurant has a cost of production C(x) = 14x + 108 and a revenue function R(x) = 82.…

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Q: Find F as a function of x and evaluate it at x = 0, x = 7/4, and x = 7/2. 1-² sin € F(x) = F(0) =…

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Q: (-1,1) a N (1,1) 2

A: find the domain and range of the given graph Domain: set of x values for given function Range : set…

Q: Consider the function f(x) = 4 − 2x² on the interval [ – 2, 3]. Find the average or mean slope of…

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Q: Write the interval in set notation. [2, 6) {x | 2 < x ≤ 6} {x | 2 ≤ x < 6}   {x | 2 ≤ x ≤ 6} {x | 2…

A: Write the interval in set notation. [2, 6) {x | 2 &lt; x ≤ 6} {x | 2 ≤ x &lt; 6}   {x | 2 ≤ x ≤ 6}…

Q: Find the limit. (If an answer does not exist, enter DNE.) [1/(8 + x)]- (1/8) lim X→0 X -1/64

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Q: For the function f(x) shown below, determine lim f(x). f(x) = x² - 10 -3 - 2x for for +-←æ x -4

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Q: y 5 4 3 2 - 2 3 сл 1 2 В 5 6

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Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: Given the curve shown below, determine if the slope of the curve at x = negative, or zero. 4 3 2 O…

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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: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration

Q: Find the indefinite integral and check your result by differentiation. (Use C for the constant of…

A: To give the solution with proper explanation for the given problem. To find the indefinite integral…

Q: - 7. Find the area bounded by the curve y² + x − 4y = 5 and the y — axis

A: We have to find the area of the given curve and line.

Q: d the equation of the tangent line to the curve y = 5x cos x at the point (7, e equation of this…

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Q: Answer all of the questions below about the function f(x) graphed below when x = 5. 8 8 f -10…

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Q: Suppose that the position of a particle is given by s(t) = 5t³ + 6t+9. (a) Find the velocity at time…

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Q: A line passes through points A(-1,-5, 9) and B(8, 5, - 15). A vector equation for the line is 7=(-1,…

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Q: sinx/(4+cosx)

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Q: Use differentials and the graph off to approximate the following. (Round your answers to three…

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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

Q: Consider the function f(x) x² + 7x + 12 2-5 a. Find the first derivative. f'(x) = b. List any…

A: Solution is here

Q: or the equation, find the slope m and y-intercept (0, b) (when they exist). (If an answer does not…

A: An equation of the form y=mx+c called slope intercept form of line where slope = m and y-intercept =…

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

A:

Q: Find the slope of the tangent line to the curve 2x² 4xy + 4y³ = 10 at the point ( − 1, 1).

A: SOLUTION-

Q: 2. Captain Crunch wants his airplane to travel along a path that is [N60°W] with a groundspeed of…

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Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

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Q: 00 3) Use the integral test to determine whether the series k=1 ke-2k diverges converges or

A: We have to check weather the given series is convergent or Divergent in nature.

Q: Find dy dx dy if y dx = x³ + 8x + 6 x² - 5

A: Given: y=x3+8x+6x2-5

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

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

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: dr Let A be the area of a circle with radius r. If dt = 2, find dA dt when r = 4.

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Q: A piece of cardboard measuring 10 inches by 8 inches is formed into an open-top box by cutting…

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Q: The graph of y=f(x) is shown below. Find the values of f(x) for x=0,x=3 and x=6

A: Here we have to find the values of f(x).

Q: Determine whether the function is differentiable, continuous, both, or neither at the value where…

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