wing using properties from the class notes (do not assume any particular vectors for u and v). Show your work! u xv|| 1. V projuv||

Q: 10z Sketch the region enclosed by y = 5, y = el, and a = 1. Find the area of the region.

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Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

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Q: y = x² and x² = y

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Q: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

Q: Step 4 of 4: Find lim f(x). x-3 Enable Zoom/Pan 10 -5 10 Keypac Keyboard Shortc Selecting a radio…

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Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: Sv x² - 36 dx

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Q: 1- 2- 3- 3-Evaluate the integrals in Exercises: [ sect? (x - 1) dx sech² s sech Vt tanh Vt dt Vt…

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Q: 3. Evaluate 5 sin rdx B

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Q: QUESTION: 2. Sketch the graph and solve for the volume of the solid generated by revolving along the…

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Q: ol Down: Two Reflections . Graph the function g given by g(x) = -f(x). 2. Graph the function h given…

A: Reflection

Q: Q3. Evaluate the following integrals 1) cothx.csch²x. dx (50-3x - W√x++) de

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Q: Can the Squeeze Theorem be used to determine lim f(x) when I(x) ≤ f(x) ≤ u(x) on (7,8) U (8,9) and…

A: In this question, we will see the properties of squeeze Theorem.

Q: 5 Given h(x) = x³ + px² − x − 4, find a value for p so h(x) has an inflection point at x = -4.…

A: I am attaching image so that you understand each and every step.

Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

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Q: Use linear approximation, i.e. the tangent line, to 1 1 approximate as follows: Let f(x) = and find…

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Q: Q1. Construct the reduction evaluate Ssind in ndx and use it to Qala) Use the inverse function…

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Q: Radium decomposes at a rate proportional to the amount present. If half of the original amount…

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Q: Calculate the are bounded by the curves: B. y = ln x and x - y - 4 = 0

A: Here we get help of graph to find the point of intersection of the given curves.  Area bounded by…

Q: 1. Given f(x)=x+5 and g(x)=x²+8x+15 Sketch the graph of y=- _f(x) g(x) Mark the asymptote(s),…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 12 -…

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Q: Let D be the region enclosed by y = sin(x), y = cos(x), x = 0 and = . The volume of the solid formed…

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Q: The vector result of (ì − 2j +3k) · (−2ī + 2j − 2k) is a. -i + 7j b. -i+j-k d. j+7k e. -i+7k c.…

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Q: A Prove that 1 B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x²+y²…

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Q: 2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. x--4 (a) lim f(x)g(x) x-4 (b) lim…

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Q: Given A(1,3,-7) and B(0, 2,-4), the magnitude of AB is a. √147 b. 3 C. √11. d. 3.3

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Q: 8- Find the derivative of (x²+1)x

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Q: In the 2000 U.S. Census, a small city had a population of 50,000. By the 2010, the population had…

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Q: √x² - 36 dx

A: Reduction Formula :    ∫secn(u)du =n-2n-1∫secn-2(u)du+secn-2(u) tan(u)n-1

Q: Use the binomial theorem to expand the binomial. (5x+2)4

A: Please refer to the image below

Q: Q1: Find the general solution to the following differential equation: y"-2y'+y=x²-1

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Q: (b) Prove that the improper integral ]] converges. dr dy (1 + x² + y²)³/2

A: Given problem:-

Q: √√3+ rdr then 0 (2)=√√3+230 I X

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Q: A parallelogram has an area of 200 cm². The side lengths are 90 cm and 30 cm. Find the measures of…

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Q: Find the value for k so that the function will be continuous at x = -4. f(x) = 7x + 47 -x² + 18x81+k…

A: Topic = Functions

Q: xy h) log₂ = Z i) log2 (2/2) =

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Q: 2. Evaluate x sin ædr using integration by parts.

A: Given: I=∫xsinxdx   We know the basic integration formula. ∫sinxdx=-cosx+C∫cosxdx=sinx+C

Q: Set up the integral to find the area of M, using vertical ectangle. Let M be the region bounded by…

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Q: x 0/x 6+29r² SS S 0 0 0 Evaluate the cylindrical coordinate integral The value is 247 960 (Type an…

A: This question can be solved using the concept of triple integrals.

Q: 8 kg/m, where x is measured in meters from one end of the rod. √x+1 The linear density p in a rod 3…

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Q: Find the equation of the tangent line to the polar curve r = 2 – sin(θ) at θ = π/3. Draw

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Q: Use logarithmic differentiation y = (x) ²

A: Topic = Derivative

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

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Q: Find ď²y dx² x = 3 sin t in the parametric equation y = 3 cost 0≤t≤ 2π.

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Q: A population of birds on an island is initially 380 birds, and it doubles (or grows by 100%) each…

A: It is given that initial population of birds on an island is 380. Each year population of birds gets…

Q: thi Prove that the improper integral } ] docdy (1 + x² + y²) ³¹²/₂ Converges

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Q: 1 Find the first five non-zero terms of the Taylor series for f(x) = - X Written compactly, this…

A: Taylor Series for f(x) centered at x=a is given by f(x) = f(a) + f'(a)1!(x-a) + f''(a)2!(x-a)2 +…

Q: y = lnx and x-y-4 = 0

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Q: Calculate the area and show the graph of the curves:

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Q: The number of tree species S in a given area A in a forest reserve has been modeled by the power…

A: Given, S(A)= 0.882(A)0.842 Differentiation w.r.t A we have, S'(A)= 0.882(A)0.842