Exercise 2.6 Find derivatives of the following functions: i. y = ln(x²+2x+3) iii. f (t) = 1 e2t == ii. g(0) In|cos | iv. h(x) = √e5x

Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z over the curve c(t) = (et,…

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Q: Help

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Find the area of the region. interior of r² = 36 cos(20)

A: Step 1: put r=0 and calculation of angle  Step 2: Angle Q  Step 3: put the limit of integration…

Q: Question 17. Use logarithmic differentiation to find dy for the implicit function た dx (1+x)5 (1 −…

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Q: Find the general solution of the system with the following equations. dx dt dy dt = 3x-7y and…

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Q: ☐ ☐ 1. Approximate the following integrals using the trapezoid rule. (Round answer to three decimal…

A: 1).ans:- method  We can follow below steps to find the solution: i). Calculate the width of each…

Q: Determine the sum of the following series. 8 n=1 (1)n-1 6n

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Q: The function  S(t) =  1 2 gt2  gives the distance that an object falls from rest in t sec.…

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Q: Follow the graph, I mean answer the question in photo.

A: Step 1: Given  f′′(x)=12x2+6x−4x+C Integrating:…

Q: Find the area of the surface. the helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v)…

A: Step 1: ** Area and Surface Integral:** A surface integral can be used to determine the area of a…

Q: Use cylindrical coordinates. Evaluate 2 [S] √x² + y² dV, where E is the region that lies inside the…

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Q: Let a = (4,6,5) and b = (3,1,1) be vectors. Compute the cross product a × b. ax b = ,

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Q: (a) Consider the graph of a function y = f (x) that passes through the points listed in this table:…

A: Step 1: Write the formula for the trapezoidal rule If we want to estimate the area under the curve…

Q: Sketch a graph of the polar equation and find the tangent lines at the pole for 0 ≤ <π r = 5 sin(20)…

A: First, note that (sin(2θ)) completes one full cycle from  (0) to (2π) as (θ) ranges from (0) to…

Q: Find a formula for the general term a of the sequence, assuming that the pattern of the first few…

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Q: 3. h(2) = re* (a) Determine the domain (b) Determine if the graph has any asymptotes, or any kind(s)…

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Q: If y = ex " then find d" y == dx"

A: Note that the derivative of exponential function eu is as follows:dxd​eu=eudxdu​ If y = enx, let us…

Q: 2. Graphing Calculator allowed: A particle moves along a straight line. For 0 ≤ts 5, the velocity of…

A: a) To find the values of  t  in the interval 2≤t≤4 for which the speed of the particle is 2, we…

Q: Use partial integration to derive that from image without deriving the right side. Here one can…

A: Let's prove, ∫xtan2xdx=xtanx−21​x2+ln∣cosx∣+C We can use the formula : ∫u dv=uv−∫v du Let's perform…

Q: 2

A: Step 1:Step 2: Step 3: Step 4:  Thanks....

Q: *Use First Derivative Test

A: Let length be x meters and breadth be y meters.xy=1200y=x1200​Total cost of fencing is…

Q: Find the derivative of y y = log2s e-logs√x (-x-1)/(xln5) ○ (x-1)/(xln5) (x-1)/(2xln5) ○…

A: Step 1: Step 2: Step 3: Step 4:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: Step 1: Step 2: Step 3:

Q: Find the average rate of f (x) = (x + 1)² over [-1, 2]. 5/3 2

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Q: If C is given by (t) = (cost, sint, t), 0<t<T, then Lyds is 02√2 O√2 O None of the above

A: If you have any problem let me know here in comment box for this thankyou.

Q: Question 3

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Q: A stock's return has the following distribution: Calculate the stock's expected return and standard…

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Q: Ay 4000- 3500 3000 G 2500 2000 1500 1000 500 0- 0 2 4 6 8 10 12 Years after 1980 14 The blue curve…

A: From The Graph, In 1988, t=8At t =8,f′(t)=300 billion per year.

Q: 2. Evaluate and simplify f(x)=x²+5x-2 for: a) f(-2)= b) f(-4x)= c) f(x+3)=

A: For any query with the solution, please ask in the comment box.

Q: Let f(x) = x², and compute the Riemann sum of f over the interval [8, 10], choosing the…

A: Step 1:Step 2:Step 3:

Q: 5 √² Using the method of u-substitution, (4x-7)² dz- f(u) du where u = du a = b = f(u) == The value…

A: Given:I=∫25​(4x−7)2dxLet u=4x-7Therefore,dxd​(u)=dxd​(4x−7)dxd​(u)=4dx=4du​Also,u=4x-7, when x=2,…

Q: Q5

A: 1. First, we look at what's under the line in the integral2. We make it simpler by changing it into…

Q: A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the…

A: The given revenue function is: R(x,y)=110x+160y−3x2−2y2−xy Find the partial derivative of R with…

Q: Use the substitution u = √(x) to calculate the indefinite integral from image.

A: Given:∫x​+x​3dx​First, we need to simplify the denominator, we have:=∫x​+(x​)2x​1​dx=∫x​+xx​1​dxWe…

Q: 2.8

A: Step 1: Step 2: Step 3: Step 4:

Q: When estimating distances from a table of velocity data, it is not necessary that the time intervals…

A: Step 1: Step 2: Step 3: Step 4:

Q: 00 n=1 (-1) "200 n0.7 For the series below calculate find the number of terms n that must be added…

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Q: Please see image

A: The statement you provided is a consequence of the Monotone Convergence Theorem. Monotone…

Q: d) -1 2(1 + 1)d

A: Ans:

Q: Please do the following questions with full handwritten working out.

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Q: Please see image

A: Solution- a) Counterexample for statement (a):Consider the sequence an​=(−1)n. This sequence…

Q: 2) A balloon advertising an open house is stabilized by two cables of lengths 20 ft and 30 ft…

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Q: Solutions to question 4 please

A: Step 1:Step 2:Step 3:

Q: ☐ ☐ 3. Approximate the following integrals using the trapezoid rule. (Round answer to four decimal…

A: Question 3.Step 1: Trapezoidal Rule (Approximation)Average of Left and Right Endpoints…

Q: (a) Evaluate the integral 2 32 -dx. x² +4 Your answer should be in the form kл, where k is an…

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Q: Please answer parts a and b

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Q: 24. Write a vector (-3, 22, -3) as a linear combination of the vectors (-1, 2, 3) and (0, 4, -3).…

A: 24)  (−3,22,−3)=a(−1,2,3)+b(0,4,−3)(−3,22,−3)=(−a,2a,3a)+(0,4b,−3b)(−3,22,−3)=(−a,2a+4b,3a−3b) To…

Q: t (minutes) 0 10 18 22 30 v(t) (meters per minute) 0 150 230 -100 200 Cameron jogs along a straight…

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Q: Homework

A: {if you have any queries please feel free to ask..}

Q: I need help with this problem and an explanation for the solution described below:

A: Dear student, please check the answers. If you have any further doubts, I will clarify them as per…