Use the definition to find the derivative f'(a) for f(x) = x+2 √x and a = 3

Q: The displacement of a particle on a vibrating string is given by the function below, where t is…

A: I am attaching image so that you understand each and every step.

Q: Use implicit differentiation with partial derivatives (as described in Example 4 page 732) to find…

A: We will find dy/dx using implicit differentiation with partial derivatives as following.

Q: IV. Given the functions f(x) = 2x + 5, g(x) = -x² - 6x + 7, and h(x) = the following. Show complete…

A: Note:- These are multiple subparts according to company guideline we can do maximum 3 subparts so i…

Q: f(x+h)-f(x) h 2. Find f'(x) using f'(x) = lim h→0 a) f(x) = x+2 for one of the following functions:…

A: Solved below

Q: Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a…

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Q: At a price of $20 there is demand for 204 items and a supply of 100 items.  At a price of $40 there…

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Q: Determine the length of the curve traced out by the vector function r(t) = (cost, sint, 4t) on the…

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Q: IV. Given the functions f(x) = 2x + 5, g(x) = -x² - 6x + 7, and h(x) = the following. Show complete…

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Q: The solution to the DE (1+x) dy -y dx =0 is O a. y = C (1+x) O b. y = c (1-x) O c. x = C (1+y) O d.…

A: Given: So,                (1+x)dy-ydx=0⇒dydx=y1+x⇒dyy=dx1+xIntegrating both sides we get,⇒ln y=ln…

Q: 1. Find the volume of the solid under the surface f(x, y) = R= [0, 1] x [1, √2] on the xy-plane. x³y…

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Q: Solve the equation for all complex solutions, giving exact forms in your solution set. -2x3 + 2x² +…

A: I am attaching image so that you understand each and every step.

Q: √r 9. lim r→9 (r - 9)4

A: Concept: The definition of a limit is the value at which a function approaches the output for the…

Q: Find the GS of y" - 4y' + 5y = 0

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Q: Consider the solid generated when the region enclosed by y = √, y = 2 and x = 0 is revolved about…

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Q: -8 --0---0--0 = -5 Given U₁ = 10 9 = -4 -8 | compute the cross products as -5

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Q: rite an expression for the nth term of the sequence. (Your formula should work for n = 1, 2, ....) 6…

A: Topic:- sequence and series

Q: 2. If g(x)=2*, evaluate the following for x: (A) g(x)=4 (B) g(x)=32 (C) g(x) =

A: We have to calculate the value of x for each function

Q: Identify which of the following is a solution to the given ODE: y' = (y-1)/2x a. y= (3/2 x)+1 b. y=…

A: We are asked to solve the differential equations

Q: Let f(x) = √58 - x = The slope of the tangent line to the graph of f(x) at the point (9, 7) is The…

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Q: Which ordered pair is in the inverse of the relation given by x2y + 5y = 9      A (2,1) B (-2,1) C…

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Q: Suppose f(x, y) = xe ²-8y². Answer the following. -8x²_ 1. Find the local maxima of f. List your…

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Q: A triangle has a perimeter of 50 cm if the three sides of the triangle are n, 4n -4, and 2n + 5

A: See the answer below

Q: A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 70…

A: Given  Speed of the circular ripple that travels outward is 70 cm/s.

Q: LEM 1: Determine the number of derivatives required for the functions to be equal to zero. y(t) =…

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Q: Let f(x) = (3x+ln(x)) / (x+3)  Find f'(x)

A: We need to find f'(x) where f(x)=3x+lnxx+3

Q: Begin with the graph of y= ex. Use transformations to graph the function. Then determine its domain,…

A: giveny=ex

Q: 5. Which of the following is the correct p(x) to use, given the First Order Linear Differential…

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Q: Consider the following. 8x² + y² = 5x (a) Find y' by implicit differentiation. - y' = 5-32x 71,6 3…

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Q: 3) Find a general solution for the following equations. b) y(3)-9y" +25y-17=0.

A: To find a genearal solution for the following equation.y3-9y''+25y-17=0

Q: dx dy A point is moving along the graph of the given function at the rate Find (in cm/sec) for the…

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Q: what is df=

A: As you ask about df so i am only defining it.

Q: Find the directional derivative of f(x,y)=sin(xy) at the point P0(sqrt(π),sqrt(π)) in the direction…

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Q: Normalize the vector v₁ Resulting Unit Vector: 2).

A: Find the magnitude of the given vector and divide the vector with the magnitude

Q: Find a unit vector n that is normal to the surface 4z² x - 2y = 46 at P = (2, 1, 4) that points in…

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Q: Let f(x) = (3x+ln(x)) / x+3  Find f'(x)

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Q: For the DE part of the solution shown below, next step would be to use y ln xlny dx + dy = 0 [yln…

A: Product Rule of Integration : ∫u.v dx = u.∫v.dx - ∫(dudx∫v.dx)dx .

Q: When hired at a new job selling jewelry, you are given two pay options: Option A: Base salary of…

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Q: Experiment 1: Slide the blue circle on the parabola to the point (-2, 4). 1A. Does the slope of the…

A: Here the parabola having the formula y=x2-x-2, we need to draw the tangent at the point (-2,4) to…

Q: Determine the x-value of all critical points for the following function. 2 X² X-7 f(x) =

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Q: Which ordered pair is in the inverse of the relation given by x²y + 5y = 9? (2,1) O (-2,1) O (-1,2)…

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Q: Use the divergent test to analyze the given series. Each answer should either be the serie diverges…

A: NOTE: Refresh your page if you can't see any equations. . use the series integral test: if an is…

Q: Choose... cos y = (x sin x - cosx+c) cos y dy = -x sec x dx sec y sin y dy = -x cos x dx (x sinx-cos…

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Q: Find the direction N from P0(sqrt(π)/3,sqrt(π)/2) in which the function f=sin(xy) increases most…

A: Given the function f(x, y)=sin(xy) Find gradient of function…

Q: Determine if the differential equation (2xy^2 + 3x^2)dx + (2yx^2 + 4y^3)dy = 0 is exact. If the…

A: As we know that: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. Then the…

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x², (0, 3)…

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Q: 3) Find a general solution for the following equations. c) y(4) + 8y" + 16 = 0.

A: The objective is to find the general solution.

Q: A bakery sells cakes. at a price of $20 per cake, it sells 300 cakes per week. At a price of $50, it…

A: NOTE: Refresh your page if you can't see any equations. . x=price per cake y=number of cakes from…

Q: The series is absolutely convergent on the following interval. x-5 <1 |x - 5] < 10 x € (-5, 15) An…

A: Given series ∑k=1∞(-1)k10k(x-5)k

Q: 10 sin(0-5) 0-5 02-20-15 6. Find lim

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Q: Suppose f(x, y) = xe -8x²-8y² Answer the following. 1. Find the local maxima of f. List your answers…

A: Detailed solution is given below