Find the equation of the tangent line of y = 4e* at xo = 0. (Use symbolic notation and fractions where needed.) equation of the tangent line:

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Q: Find the inflection points of each of the given curve.  y = x3 – 3x2 + 4

A: ⊙a function y=f(x) is said to have inflection point at x=a, if its second derivative i.e. d2ydx2 cha...

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A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

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A: Given: 1: y=3cosx+2sinx2: f(t)=t sint   To Find: 1: y'2:f'(3π2)    

Q: Find the equations of all tangent lines to the graph of y=x -7 x+ 49 that pass through the origin (0...

A: Equation does not passing through origin.  Hence there are no tangent line whose passing through ori...

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A: Given:        Absolute convergence:          A series ∑an converges absolutely if ∑an converges.    ...

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Q: INTEGRAL Evaluate the following: S(a- S (a – x)-³dx 3.

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Q: Since (k + 1)³/3k+1 ki3 /3* (1+ ±)* _ 1 lim k→+0 lim k→+∞ 3 3 the series (converges/diverges/inconcl...

A: The given series,       ∑k=1∞k33k

Q: The temperature, in degrees Celsius, at a point (x,y) on a metal plate is given by T(x,y) = 20-4x^2 ...

A: Given Temperature on a metal plate at point (x,y)T(x,y)=20-4x2-y2

Q: d. lim f(x) e. lim f(x) c. lim f(x)

A: d.limx→2+f(x)= ?f(x)=2x ; x≥2limx→2+f(x)=limx→2+ 2x=2×2=4limx→2+f(x) =4e.limx→2-f(x) =?f(x)= x ; 1≤x...

Q: Let A, B and C be any sets. Which of the following is equal to (A U C) n (B \ C)? Select one: a. (A ...

A: Solution is given below:

Q: INTEGRAL Evaluate the following: 8. Se2×dx

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Q: Suppose Gavriel's utility depends on the amount of time spent playing on Xbox (X) and the amount of ...

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Q: Determine whether the series converges. 00 Σ k=1 V7k – 1 O The series converges. O The series diverg...

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Q: Make 3 unique examples of domain and range in real life scenarios. Please highlight the domain and r...

A: To write: 3 unique examples of domain and range in real life scenarios.    

Q: dx x2 (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb in...

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: Find the area of the region bounded by the curves y = x, x = 1 and y = 0. %3D A. 1 В. C. 1 3 D. 1 4 ...

A: Area = integration of upper curve - lower curve and put the limits.

Q: For the function (1- x if x 1 evaluate the limit lim f(x). メー1 (If a limit does not exist, enter Ø ...

A: This question is based on Limits calculation of a function.

Q: Solve the given differential equation. All solutions should be found. (8y"+2x°y) dx - (7cy°+) dy = 0...

A: This is a homogenous equation.  Let y=vx

Q: 23. What is dx? 3 – e4r e2z + V3 In e2r + V3 In |e2x а. +C C. +C 2 e2x – V3 V3 /3. b. V3 +C V3 +C 2x...

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Q: 3 V1+x³ [6] S dx > x-2

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Q: Let {xn} be a bounded sequence on R. Show that Xn lim = 0. n→+∞ N

A: Given sequence {xn} is bounded we want to show that  limn→+∞xnn=0 we  use the limit limn→∞1n=0

Q: Use geometry (not Riemann sums) to compute the integral. dx 3 Enter a pumber

A: The given integral is  ∫12 x3dx

Q: 3 V1+x3 -dx x-2

A: Given:      ∫1+x33x-2dx      =∫x2 x3+13dx substitute u=x3+1                 dudx=3x2→dx=13x2du

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Q: For the next three questions, consider the differential equation: y" – 2y' + y = e* arctan r

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Q: Use technology to evaluate the given expression. Take 1.5 7.9 1.4 -2.32 5.4 and B = 5.8 0 A = \ 44.4...

A: A=1.4-2.325.444.4012.8AT=1.444.4-2.3205.412.8B=1.57.95.805.46.94.2B=4.2×1.54.2×7.94.2×5.84.2×04.2×5....

Q: Determine (without solving the problem) an interval in which solution of the given initial value pro...

A: Follow next step

Q: Use technology to evaluate the given expression. Take 1.6 7.3 1.4 -2.39 5.1 A = and B = 5.5 0 44.8 1...

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Q: Find the derivative of the following exponential functions: ans. y' = -4e-4x 1. y = e-4x ans. y' = x...

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Q: Find the length parameter of the curve r(t) = with base point at ( 7, 0, 0 ).

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (– 1)*+1 8k k=...

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Q: 2. Explain how we know the function f(x)= 2.x is one-to one. Then find the inverse function f. x- 3

A: We are asked to  find the inverse of the function.

Q: The exponential growth model of a population in a certain city is A= 20e0.05t where A is the size of...

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Q: Which of the following is the general solution to the differential equation 4xyº = -x² – y² for x> 0...

A: The differential equation is given as , 4xydydx=-x2-y2 find the general solution.

Q: Using integration by parts, uV- V du cone for j 3*crc'(3x) sin C3x ) dx solution. dv = du = V =

A: Solution is here

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Q: What is the general solution to the differential equation 2e* cot(y) dx – (4 + e*) csc²)dy = 0 ? (4 ...

A: Here, the given DE is: 2excot(y)dx-(4+ex)csc2(y)dy=0

Q: [2x+5y=7 3x + 2y = -6' 1. Solve the linear system using graphical method.

A: The given linear system,2x+5y=73x+2y=-6

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Q: Find the area that is inside both r=1−sinθ and r=2+sinθ

A: Graph:

Q: Evaluate the integral below by following the steps given. 1 xp= x2 I || 6/ a.) Show that the substit...

A: Given: I=∫19-x2dx  ...1   As we know from the trigonometric identity: sin2θ+cos2θ=1 And ∫a·fxdx=a·∫f...

Q: Use substitution to evaluate the integral | (3x³ + 5)° . 27x²dx

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Q: dy = ay + b whose dt Write down a differential equation of the form 3 as t → o. 4 solutions all appr...

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Q: 4. Figure 4.92 shows drug concentration curves for anhy- drous ampicillin for newborn babies and adu...

A: Basic calculus problem

Q: . Find the slope and equation of the tangent line to the graph of the equation at a given point. 1. ...

A: Topic:- derivatives 

Q: x1 x + dx

A: