By determining f′(x)=limh→0 f(x+h)−f(x)/h​, find f′(8) for the given function.   f(x)=2x2   f'(8)=

Q: Evaluate the triple integral given II: 0≤x≤ 2, 0≤ y ≤ 3, 0≤ z ≤ 2. [[[x³y²z² dx dy dz a) 76 b) 128…

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Q: Find the equation of the surface in cylindrical coordinates, given the equation in Cartesian…

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Q: What is the general solution to the equation a cos2x = 0? In the answers, n is an integer.…

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Q: As was mentioned in Problem 24, the differential equation (7) that governs the deflection y(x) of a…

A: We have to find the solution.

Q: clnx 5) cos et dt = d ftm a) COS X x b) cos(ln(x)) c) cos ex d) cos 1

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Q: Find dy/dx.  y=7x

A: Use the basic result of differentiation.

Q: 2. Find two numbers whose difference is 100 and whose product is a minimum.

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Q: Help me Solve the following(step by step) a) 3-4|x+3| ≥ 1 b) |x^2| +5=0 c) x^2 +4x=2x+4 d) 6-2x>-x

A: (a).The given inequality is:3-4x+3≥1

Q: Two poles are connected by a wire that is also connected to the ground. The first pole is 20 ft tall…

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Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. Find the gradient of f(x, y,…

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Q: Find the Taylor polynomial p₁(x) for f(x) = ln (3x) at x = 1.

A: Given: fx=ln3x To find Taylor polynomial at x=1 We know that ddxlnax+b=aax+b

Q: Give a rule of the piecewise-defined function. Give the domain and the range. What is the rule?…

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Q: f(x) = 36x + 3x2 - 2x3 a) Find the intervals of increase or decrease b) Find the local maximim and…

A: see below the answer and calculation As per Bertleby Guideline I have to solve first three subparts.…

Q: For the function, do the following. f(x) = 3/1/2 from a 1 to b = 3. Approximate the area under the…

A: We have to find the area using the two methods 1)Riemann sum using 10 rectangles 2) using definite…

Q: Consider the piecewise function 5t - 5 5 cos(-5t) -5-6e5t -5 sin(5t) f(t) = = t< -11 -11 ≤ t < 3 3 <…

A: For a piecewise function we can write it as a unit step function as f=f't&lt;af''a≤t≤bf'''t≥bThen…

Q: Evaluate the integral using cylindrical coordinates: fff³ 3 sin(x² + y²) dx dy dz

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Q: (1) If f(x) = = x², then f'(x)= (3) If h(x) (2) If g(x) = - 6x5, then g'(x) = = 1 = I then h'(x) =

A: formula used is   dxndx=nxn-1d dx(constant)=0

Q: Calculate all four second-order partial derivatives of f(x, y) = 2x²y + 4xy³. = || = )= ||

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Q: 7. f'(m) for f(m)= 1 sec(2m) 9. f"(x) for f(x) = 3x-25* 11. f'(I) for f(T) = BT + rº 1-B dy 13. 3. d…

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Q: X 2 1.5 10.500.5-11.52 -2 y -1.5 -1 -0.50 0.5 1 1.5 2 14 13 12 Z 11 10 Find the surface area of the…

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Q: Find the partial derivatives of the function fz(x, y) fy(x, y) fay(x, y) fyr (x, y) = f(x, y) =…

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Q: Find dy/dx. y=3x7

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Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = x² from…

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Q: Find indicated rate of number 3

A: Topic:- application of derivatives

Q: The inverse Laplace transform of -7s F(s) = e s² + 3s - 4 is f(t) Use step(t-c) for uc(t)

A: Let's find inverse Laplace of given function.

Q: Suppose a sample of a certain substance decayed to 63.4% of its original amount after 300 days.…

A: Let's find half life of the substance.

Q: Use integration by parts to evaluate the following integral. 1 12 S 0 x In 12x dx

A: To evaluate the given integral

Q: Find d2y/dx2. y=1/x10

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Q: se that F(x) = f(g(x)) and g(3) = 6, g' (3) = 4, ƒ'(3) = 10, and ƒ'(6) = 7. Find F'(3).

A: Topic:- application of derivatives

Q: (7 y² +6 x)dx + 11 x y dy=0 (*) a) Determine whether the given differential equation (*) is exact…

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Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m³/min. How fast is the…

A: Let's find height of the water increasing rate.

Q: Question 2 differential equation 2 = y² + ¾/7 y y² + y = 1: Consider the following a) Is the given…

A: The given differential equation is:1ty'+2t2y=t4e-4ty-3

Q: Find the point on the curve y = √4x + 4 which is closest to the point (7,0).

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Q: he concentration of a drug t hours after being injected is given by C(t)=0.5t t^2+59. Find the time…

A: Topic:- application of derivatives

Q: Given the graphs of f (x) in blue and g (a) in red below, find the values of the following. (a) (b)…

A: Topic = Functions

Q: Find the inverse Laplace transform f(t) of the F(s) = ln ( ² s² +81 s² + 16 function F(s) In f(t) =…

A: To find inverse Laplace transform.

Q: Let y = exp /9+9x3). Find dy/dx.

A: Given function:- y=e9+9x3

Q: K Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of…

A: To solve the integral using Simpsons and trapezoidal rule.

Q: Evaluate Your Answer: Answer [₁¹ 1 - 3x √x dx

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Q: Find and prove the limit or deteremine if the limit doesn't exist: ((-1)n)/n

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Q: Determine whether the statement is true or false. (log2 9)(log9 2) = 1 True False

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Q: Question 1. equation : y cost + 2te³ + (sin t + t²e³ − 1)y' = 0. 1: Consider the differential a)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Sketch the region bounded by the graphs of the given equations and find the area of their region. X…

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Q: Find the local and/or absolute maxima and minima for the function over the specified domain: y=x+1|…

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Q: For the function, do the following. 1 f(x) = 2x from a = 2 to b = 3 Approximate the area under the…

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Q: Consider the following. x = 3 sin(68), y = 3 cos(68), Oses" (a) Eliminate the parameter to find a…

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 300 + 700t - 120t², where t…

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Q: Calculate lim x →0 sinh(2) — x3 X

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Q: x 6) Find the average value of f(x) = √x²+16 on [0,3]. a) 1 b) WIT 3 WIN c) 3/3 d) 3

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Q: Find the volume of the largest right circular cylinder that fits in a sphere of radius 1. V = +…

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