Consider the following function. (If an answer does not exist, enter DNE.) f(x) = 1 + X x² (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) X = Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.) y = (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is decreasing. (Enter your answer using interval notation.) (c) Find the local maximum and minimum values. local maximum value local minimum value

Q: 1. If f(x)=5x^3+6e^x then f′(x)= and f′(0)= 2. If f(x)=5ln(x)+10/x then f′(x)= and f′(1)=

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Q: Find the normal vector to the tangent plane of z = 5e²-6y at the point (12, 24, 5). X component=

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Q: Find the shortest distance from the point P(10, 9, 8) to the paraboloid z = 9-x2 - y2. Give your…

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Q: proportion of manuscripts and rate of growth alter centuries. The proportion of manuscripts after 3…

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Q: Evaluate the integral. (Use C for the constant of integration.) J 5 tan(x) sec³(x) dx

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Q: K 5 (x+4)² + (y-40)² = 1 X Find the center and radius of the circle. (x, y) = ((-4,40) X

A: Given: x2+y2+4x-20y +28=0

Q: Find the derivative of the function. y = In (2x³ +7x) 5/3 y'=0

A: y=ln2x3+7x53d dx(lnx)=1xd dx(xn)=nxn-1lnxn=nlnx

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A: Given function is Differentiating both sides with respect to x, we get

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A: Given: The length of the interval is ∆x=b-an Here ,a=0 ,b=6 ,n=6. Let x0=0,x1=1, x2=2,x3=3,…

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Q: Find the derivative of the function. 1 + sin(t) 1 + cos(t) s'(t) = s(t):

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Q: Find dy/de by implicit differentiation. x²y² + x sin y = 2

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Q: A college student works in both the school cafeteria and library. She works no more than 12 hours…

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Q: 2. Find the derivative of the function f(x) = √√x² +6_ from first principles.

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Q: Find a tangent vector of unit length at the point with the given value of the parameter t. (3 + ť8)i…

A: Given, r(t)=(3+t8)i+t2j To find the unit tangent vector at the point t=1.

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A: Given: y=4cot2πx-π2+2

Q: Evaluate the integral. (Use C for the constant of integration.) St t5 In(t) dt

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Q: In problem do the following. (a) Choose the appropriate substitution for r in terms of using the…

A: To evaluate the following integral. ∫1x2+2x+22 dx

Q: Evaluate the limits, if they exists. (If an answer does not exist, enter DNE.) (A) lim h → 0 (sq rt…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: For the following graphs of rational functions, find the equation: 1. M w+ vit 67 2. 716 -6

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate the integral. |5 50 tan² (0) de

A: Given: ∫5θtan2θdθ Let I = ∫5θtan2θdθ Start by using the trigonometric identity: sec2θ-1=tan2θ…

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A: ekx=0.5we know lnxn=nlnxlne=1

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Q: ==³-187² +811. lowing describes the entire set of 7 values where the curve is decreasing?

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A: Given equation:- y2=2x3+7x2

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A: The details solution of the given question is given below in step 2.

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Q: FINAL

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Q: Differentiate the function. G'(q) = = G(q) = (6+q-¹)²

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Q: For the function h(x,y): dh Əx || 9x + 5y 4xy-7' find and dx

A: Given: hx,y=9x+5y4xy-7   We know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2

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A: Given that , drdt=5 ft/secr=2 feet find dAdt=?

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Q: Find the indicated higher order derivatives of the following functions: 1. Find all derivatives of…

A: To Find :  Derivative of the given functions.

Q: Estimate the value of 15¹/4 using differen- tials. 1. 15¹/4 2. 151/4 3. 151/4 4. 15¹/4 " 22 22 16 65…

A: let f(x)=x14f(x+∆x)=f(x)+f'(x)∆xx=16, ∆x=-1

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A: No, it is not possible for a 5x5 matrix to be invertible when its columns do not span R5 (the…

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A: Given integral:- ∫0151-x2dx

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Q: dy Find when 5x² + 3x³y - 5y³ = 28. dx dy dx x(9xy+10) 3(x-³-5₁2) The slope of the tangent line to…

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Q: Let f(x)=3e^x+4+e^−4 f′(0)=

A: d(ex)dx = ex

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Q: Calculate the area between f(x) = 2x + 4 and the x-axis, between 0 and 4, you get:

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

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Q: User = }= * 3 – 5 2t to parameterize the equation: y t+ TI t²³ + +²2² +

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Q: Q1. (a) Show that the following table represents a linear function. 0 4 10 f(x)-26 18 x (b)…

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Q: Consider the following functions. f(x): = 2x + 5, g(x) = 4x 1 Find (f o g)(x). 8x + 3 Find the…

A: Given f(x)=2x+5g(x)=4x-1   We are required to find(fog)(x)Domain of (fog)(x)(gof)(x)Domain of…