1 Find "(x) if Ax) -. %3D X+1. 1 (x+1) (x+ 1) -2 (x+ 1)3 12

Q: 8. Find the derivative of (logsx?). dx 2 A. x In 5 1 В. x In 2 С. x In 5 D. 2x In 5

A: Solving the problem by finding the value of the derivative. For the question no 8. Option A is…

Q: Find the coordinates of all points on the curve x^2 -2y^2 = 5xy-33 where the curve has a horizontal…

A: x2-2y2=5xy-33 →(1)Horizontal tangent slope is 0Differentiate (1) w.r.t…

Q: Determine if the improper integral converges or diverges. Find its value if it converges. Show…

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Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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Q: Approximate the critical numbers of the function shown in the graph. Determine whether the function…

A: Explained below

Q: Evaluate the following limit: (x- 2)2 – 4 | lim If it does not exist enter DNE.

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Q: 1. The derivative of the sum or difference of two differentiable functions is to the sum or…

A: The solution is given in the next step.

Q: CoS cos³ 0 5./ d0 1-sin0

A: Given problem:- ∫cos3(θ)/(1-sin(θ)) dθ

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: Determine if the given series is convergent or divergent. 3" en – 2" n=1 2.

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Q: Each of the regions A, B, and C enclosed by the graph of f and the x-axis has area 6. Find the value…

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Q: Question Consider the function f(x) below. Over what open interval(s) is the function decreasing and…

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Q: Evaluate the following limit: x² + x- 2 lim- x-1x2- 2x + 1 If it does not exist enter DNE. Round to…

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Q: Find the points on the curve y= (x-1)(x -4) where the tangent line is parallel to y= -4x, O (3, 10)…

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Q: Find fy (x,y) if f(x.y) = (x° +y®)* fxy (X.y) = %3D

A: Topic = Derivative

Q: (-3)"(x – 2)" Consider the power series Vn+2 Use Alternating Series Test to show that the series…

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Q: Evaluate the following double integral over the region R. 7 x-y') dA; R= {(x,y): 0<xS1, -1sys1}…

A: Here we have to evaluate the given double integral over the region R .

Q: Compute f'(a) using f'(a) = lim f(a + h) – f(@) or f'(a) = lim Tx) – J(d) for f(x) = 15x³, a = 2. or…

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Q: ) Solve the D.E dy + (xy – xy²)dx = 0

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Q: c(x)=2x2-7x; c(0)=4,000

A: answer is in next step

Q: f(x,y) = 5 + Vx – y² +4

A: To determine theb domain and range of the following function.fx, y=5+x-y2+4

Q: 4. Find the Laplace transforms of the functions: (a) f(t) = t² (b) f(t) = t – 2e3t

A: a) f(t)=t2b) f(t)=t-2e3t

Q: Find parametric equations for the line whose vector equation is given. (а) («, у) %3D (3, —3) + t(1,…

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Q: 6. Use Laplace transforms to solve the initial value problems: (a) x" + 9x = 0; x(0) = 3, x'(0) = 4…

A: Given x''+9x=0, x0=3, x'0=4

Q: Q3) Evaluate triple integral , dz dx dy.

A: We can calculate this as follows:

Q: LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 1. (9Dª + 6D³ + D²)y = 0 2. (4Dª – 45D² – 70D – 24)y = 0

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Q: d What modificatioIis would have to be made to find the derivative sin 6 if0 is given as dx an angle…

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Q: +0 (2х — 1)" n V4n + 1 n=0

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Q: E. Consider two functions f and g on [0, 7] such that I f(x) dr = 9, g(x) dr = 6, (2) dr = = 4, |…

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Q: dy_ 1-y dx V1-x? V1-x' +/1-y? = a(x - y), then show that %3D

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Q: d -sin ở if0 is given as What modifications would have to be made to find the derivative - an angle…

A: Let's find.

Q: Let a = ci + jand b = 16i + 12j. Find c so that the angle between a and b is Round your answers to…

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Q: 4) V9-z zt2-6

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Q: Find the volume of the given solid over the indicated region of integration. f(x.y)%3D4X+5y+7;…

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Q: Convert dzdydx Into an integral of spherical coordinates 6coso S6 SR psinødpdød0 psinødpdøde Option…

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Q: х2 — бх + 9 dx Убх — х2

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Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: (Basic Differentiation Rules Basic Calculus) Kindly answer 1-3 and show complete solution. thank…

A: Formula:ddx(a f(x))=a  ddxf(x)ddx(xn)=n xn-11)f(x)=10 x10f'(x)=10 ddx x10f'(x)=10 10 x10-1f'(x)=100…

Q: Description Evaluate the volume of the solid generated by revolving the plane region about an axis.…

A: Note:As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Determine whether the following functions below is a solution or not a solution of the integral f(1-…

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Q: A. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 5. (2D* – 3D3 - 2D²)y = 0

A: According to Bartleby guidelines I can only answer the first question of the given two questions.…

Q: V. Let f(x) be a differentiable function such that for all æ > 1, • f(x) > 1, • f'(x) < f(x) and lim…

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Q: eries 1)" 2 + 5 rmine if the resulting series of constant terms wh ely convergent, conditionally…

A: We have to find the following conditions according to the given information

Q: The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

Q: Consider the parallelepiped with adjacent edges u = 9i + 5j + k v = i+j+ 8k w = i+ 2j + 8k Find the…

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Q: In(arctan(x)) dx 1 + x2 1

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Q: In item number 5, the integral of Sx3 dx is obtained by applying what Basic Theorem of…

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Q: Question 2:- Applying the properties of logarithms to simplify expressions a. logs 8 + logs 1 b.…

A: This can be done as follows:

Q: (b) Repeat part (a) using 3 subintervals and the velocity at the midpoint of each subinterval. mi

A: answer is in next step