Find the slope of the tangent line to the curve y = √x + 2 at the point (2,2) using the definition of the derivatives.

Q: Suppose that the position of a particle is given by s(t) = 3t³ + 2t + 9. (a) Find the velocity at…

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Q: x²y² 4 (x,y)→✈(0,0) x² + 3yª Show that the limit does not exist lim

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Q: - Drug pharmacokinetics A patient takes 150 mg of a drug at the same time every day. Just before…

A: we need to find the quantity of drug.

Q: True or false. The integral True -1 False 3 2 1 -1 f(x)dz gives the area of the shaded portion…

A: Here we have to verify whether the given integral for finding the area is true or false.

Q: Find the area of the region between y=-x² + 4x and y = 4 from=0 to x = 2 Simplify your answer. Type…

A: NOTE: Refresh your page if you can't see any equations. . given functions are limit of x is  so…

Q: The half life of a substance is 49 years. If there are 220 mg present now, how much will remain in…

A: The half life of a substance is 49 years. If there are 220 mg present now, then to determine the…

Q: Solve using Lagrange multipliers. (The stated extreme values do exist.) A one-story storage building…

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Q: A rectangular sheet of metal 24 cm long and 12 cm wide is to be transformed into an open box by…

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Q: Find in sin (1 + 2x) + xy = ecosy dy d.x

A: Find derivative

Q: I company determines that its demand function is given by p(q) = - 0.7q + 2406 and that its cost…

A: I company determines that its demand function is given by  pq=-0.7q+2406 and that its cost function…

Q: Find the derivative of y with respect to z. y=7 (25) dy dz ||

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Q: The graph of y=r(z) is given below. Answer each of the questions below the graph. -9-8-7 -6 -5 -4 -3…

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Q: Give the substitution that converts the given nonlinear equation into a linear equation then find…

A: Given Differential equation y' - y = -y2

Q: A thermometer inside a room reads 22°C. The thermometer is relocated outside the room. After one…

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Q: person's weight increases with height through approximately the end of the teenage years. Dan's…

A: Given query is to find the weight when height is 57.5 inch.

Q: You've decided to sell sweatshirts for the upcoming game. You project that at a price of $32.92 por…

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Q: Question 10 Find the indefinite integral. In 5x finx. dx

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Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 7 sin(x). If f(0) = 4 and ƒ'(0)…

A: Given: f''(x)=7x+7sin(x), f(0)=4 and f'(0)=3

Q: Consider the following parametric equation. a. Eliminate the parameter to obtain an equation in x…

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Q: Determine the absolute extreme values of: | f(x) = = 4x³+108 X on (0, ∞)

A: To find the extreme value of given function

Q: What is the maximum value of f(t) = sint + cost in the interval 0 ≤ t </ √2 2√2 01 2

A: The given function is; f(t)=sint+cost

Q: What is the distance between the focus and directrix of the arabola y² – 8x – 2y + 1 = 0? 2 0 1 4 8

A: we will find the required.

Q: Consider the following table, and assume that f(x) and g(x) are differentiable functions with values…

A: Let's find value of h'(4).

Q: - 1 Find ²¹ dz x² +C

A: As we know that, The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And use…

Q: x-3 →3 x² +1° If the limit does not exist, type DNE. Compute the limit lim

A: Here is the solution

Q: Evaluate the derivative of the following function. f(x) = (2x)³x f'(x) = (Simplify your answer.)

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Q: y=3-vr+2 +++ + ++++x

A: Let's draw a graph by using transformation.

Q: Which of the following statements about limits is inaccurate or false? Choose all that apply. Limits…

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Q: A curve with polar equation T 19 5 sin 0+31 cos 0 represents a line. This line has a Cartesian…

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Q: 4. y (x+y) dx + x(x²-5y³)dy = 0, y(a)=1

A: Please see the below picture for detailed solution.

Q: Number of equal real root(s) Number of unequal/unique real root(s) Number of imaginary roots Number…

A: We need to interpret the function and graph.

Q: Consider the following: f= x³ + 3x² + x - 2. Without solving for its roots, we can say that there is…

A: Given query is to find the statment is True or false.

Q: Consider the following table, and assume that f(x) and g(x) are differentiable fund as given. X 1 2…

A: Given query is to find indicated derivative.

Q: Find the area under the curve y=f(x) = 4x-4x² on the interval [0, 1]. Enter your answer as a…

A: Given query is to find the area under the curve.

Q: Find the Laplace transform of the following functions. 10. f(t) = sinh t-t² cos5t t

A: Given function:- ft=1tsinht-t2cos5t

Q: The population of a city is 85,000. If the population is declining by 2% per year (not a continuous…

A: Given initial popiulation of the city ( P0 ) = 85000 If the population is declining by 2% per year

Q: Given that the graph of f(x) passes through the point (4, 7) and that the slope of its tangent line…

A: use derivative  as slope and use the integral for finding the value of function .

Q: Two airplanes are flying in the air at the same height. Airplane A is flying east at 481 km/h and…

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Q: For this function there are two important intervals: Consider the function f(x) = 8(x-4)²/3 (-∞, A)…

A: We need to find out the critical numbers and also need to find out the intervals where function is…

Q: Consider the function f(x) = 7 6 1-9 3 x7 of f(x) with F(1) = 0. Let F(x) be the antiderivative Then…

A: The given function fx=7x3-6x7. We have to find the antiderivative function Fx.

Q: turning points show all work y(x)=2x^4-10x^2+8 y(x)=(x+1)(x-2)(x+3) y(x)=-(x+1)^2(x-3)

A: we have to find turning points of given curve :- 1 .  y(x) = 2x4-10x2+8now ,…

Q: Sketch the regen enclosed by y=2x and y-axe find the area of the region.

A: The solution to find the area and curve of given is as follows.

Q: z1 and z2 in polar form. (Express ? in radians. Let 0 ≤ ? < 2?.)

A: since we know that if  z = a + ib be complex number then its polar form be z = r cosθ+isinθ   where…

Q: What comparison series would you use with the Comparison Test to determine whether Choose the…

A: Series

Q: Obtain the particular solution of the following: (SEPARATION OF VARIABLES) 2. 2y dx = 3x dy; when x…

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Q: √ d (268)6 This can be transformed into a basic integral by letting Consider the indefinite integral…

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Q: A sheet of paper 84 cm-by-64 cm is made into an open box (i.e. there's no top), by cutting x-cm…

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Q: Given the pattern -36, 12, -4,... (a) Write an explicit formula for the pattern. (b) Write a…

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Q: Solve using Gauss-Jordan elimination. 3x₁ + 2x2 - 6x3= 2 4x1 +26x2- 72x3 = 102 X₁ + 4x2 11x3 15 -…

A: Given Equation:- 3x1+2x2-6x3=24x1+26x2-72x3=102x1+4x2-11x3=15

Q: Number of equal real root(s) Number of unequal/unique real root(s) Number of imaginary roots Number…

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