Find the area of R - region bounded by the curve y = 1/x2 and the lines y = x and y = x/8 O 1

Q: (a) If f(x) = x* + 3x, find f'(x). f'(x) = (b) Check to see that your answer to part (a) is reasonab...

A: Given: f(x)= x^4+3x f'(x) means  we have to find derivative  So, the derivative of f(x)  f'(x)= 4x^3...

Q: Find the norm ||A||. of each o

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Q: Pretzels cost $4 per lb, dried fruit $5 per lb, and nuts $9 per lb. The three ingredients are to be ...

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Q: Consider the following. if x <1 if x 21' f(x) = a = 1 (a) Find the left-hand and right-hand limits a...

A: Topic:- calculus

Q: The general solution to the initial value problem y" + 5y' + y = 0, 37 y(0) = -2, y' (0) = 7 is y = ...

A: Given that: y''+5y'+372y=0y(0)=-2, y'(0)=7y=eat(c1cos(bt)+c2sin(bt))

Q: 1-2) Use the 4 step process or the increment method to get the derivatives of the following function...

A: 1) y=4x2+3x2) y=2x-13) y=4x4+2x3-3x2+7x-15

Q: 3. Find the general solutions rounded to two decimal places for each of the following. For each ques...

A: Given :a) sin 3x= 0.72sin 3x = 12The General solution is x=(8n-7)π2∪(8n-5)π2  ∀n∈ℤ  

Q: The exam has 14 questions, and the total number of marks for the exam is 100. In how many ways can t...

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Q: Evaluate the definite integral: 6x da

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Q: Find the following using the table below. 1 2 3 f(x) f'(z) g(x) 1 4 4. 1 2 4 (x),6 h' (2) if h(x) = ...

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Q: the integral F(®) = cos*(0) + sin(20) – 3 cos(0) COS do sin (0) +3 cos2(0) + 2 sin(0) – 3

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Q: Evaluate the integral by interpreting it in terms of areas: | (4 + 32) dz : %3D

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Q: Evaluate the following integral: 1 dx 1+ 36x2 Note that an arbitrary constant has been added for you...

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Q: cos4 cos* x

A: Follow the procedure given below.

Q: Consider the function f(x) = Complete the table below and sketch its graph. x 2 |-1 |-0.5 -0.1 F(x) ...

A: Given Data: fx=x+1x2+x

Q: Find the cartesian equation of the following: 6 1. r = 3-sin 0 2. r2 cos(20) = 4 %3D 9. 3. 4 sin(20)...

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Q: At what point does the graph of 3x+y=0 and x-y=D4 intersect?

A: Given: 3x+y = 0 y = -3x And x-y = 4 y = x-4

Q: Consider the function f(x) = Complete the table below and sketch its graph. |-2 -1 -0.5 -0.1 F(x) X ...

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Q: 4 If f(x) sin z, find f' (x). Find f'(4).

A: Topic:- derivatives

Q: Compute the surface area of revolution about the x-axis over the interval [0, 2] for y = 2x'. (Use s...

A: We know that; The expression for the area of the surface revolution of y=f(x) rotated about the x-ax...

Q: Let f(x)= -6x^4+8x^3+72x^2 e) f has an inflection point at x=

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Q: E F Which blue function is the graph of the SLOPES of the red function? F

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Q: Q1. x= [5, -3, –1, 2]" is a 4-dimensional vector. Calculate the following values: 1. the squared l2-...

A: Given 4-D vector: x=[5,-3,-1,2]T We have to find the Norms of the vector. Norm is the magnitude of t...

Q: Given the following table, give the best estimate for f(12) 6. 9. 12 15 f(x) 33 44 55 63 27 7 The es...

A: Topic:- function

Q: 4- Prove that lim- tan 2x 5-lim 2(-3+x)²-18) x-0 X-0 2.

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Write the correct u and du. S. Ve 3x – 16 3e *d...

A: Given:  1) ∫3e3xe3x-164dx   substitute u=e3x-16       dudx=3e3x→dx=e-3x3du      =∫1u4du       =∫u-14...

Q: Convert the following number in the indicated base. 6701 to base 15

A: Divide the number repeatedly by 15 until the quotient becomes 0. When 6701 is divided by 15, the qu...

Q: Consider the curve defined by the equation 2x + y = 3xy for questions (4-6). %3D 2 1 -3 -2 -1 1 2 3 ...

A: The given curve is: 2x3+y3=3xy

Q: Differentiate the function after first rewriting the function Tn a different form. (Do not use the p...

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Q: the figure given, determine force P that will give the body an acceleration of 2m/s given that the c...

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Q: Ay Given y = x²+ 3x + 5, find Ax %3D Ay 2Ax + x + 3 Ay 2xΔx +x+3 Ax Ax O Option 1 O Option 4 Ду Ay 2...

A: topic - difference quotient

Q: The radius of a circular oil slick expands at a rate of 3 m/min. (a) How fast is the area of the oil...

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Q: Find f if f"(x) = 4 – 6x, f(0) = 3, and f(2) = -2. %3D Answer: f(x) =|

A: f"(x) = 4 - 6x , integrating the equation  Using the formula ∫ xn dx = xn+1 /(n+1) ∫ f''(x) dx = ∫ 4...

Q: The given two-parameter family is a solution of the indicated differential equation on the interval ...

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Q: I. Find the limits of the ff by applying the limit theorems. 6. lim vx² + 5x + 2 1. lim 2021 x→12 x→...

A: 1. limx ~12 2021, function f(x) = 2021 is independent of x limit is 2021   2.  limx~7 4x - 3 putting...

Q: Evaluate the definite integral: (4x – 4) dz

A: Evaluate the definite integral

Q: SA We have seen that the harmonic series is a divergent series whose terms approach 0. Show that 8, ...

A: Given :∑n=1∞ In1+1nClaim :To show that the series is diverges with limn→∞an=0.

Q: 1- y = vx – 1 dy 2- y = prove that (sin x) dx = cOs x

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Q: How fast is the surface area of a cube increasing when the length of the edge is 3 in and its rate o...

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Q: y(4y++ 12y²+9) *dy A (2y²+3)² 3 B (2y²+ 3) 3 ©(2y²+3) D 4y4+ 12y²+9 E None

A: We have to find integral

Q: The function gives the cost to manufacture x items. C(x) = 30,000 + 10x + 50,000 -; x = 100 Find the...

A: Given problem:-

Q: If g(x) = 3x2- 4x +5 ; G(x)=x3 – 2x2+ 5x , then G is the anitiderivative of f . A) True B) False

A: Let's find. 

Q: Determine the value/s of D if the graph of the equation 4x? + y2 – 4x + Dy = -2 is 1. an ellipse; 2....

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Q: A pebble is dropped into a still pool and sends out a circular ripple whose radius increases at a co...

A: Given query is to find the rate of change area.

Q: z = x² – y² Use this equation 1. Write the equations for xz- and yz-traces. 2. Plot (rough) the xz- ...

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Q: 21) In Problems 21 through 26 are given (xa)'= a xa-1, (x)' = 1, ( constant )'= 0, (sinx)' = cos x, ...

A: Since the student has posted many sub-parts of the question and does not mention any specific part, ...

Q: Let f(x) = 9 cos(sin(z°)). %3D Then f'(x),

A: Using the chain rule of differentiation,

Q: use newtons method for this calculus equation  show all steps f(x)=x3+2x+1

A: Given f(x) =x3+2x+1. We use Newtons Method to find a real approximate root of f(x). From Newtons Met...

Q: Evaluate S dx by letting u = x – 1. The given integral can be transformed to S h(u)du. If we evaluat...

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Q: e height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = - 1...

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