1. Find the area of the region that lies inside the cardioid T-1+ sin 0 and outside the circle r - 1.

Q: D Question 3 Let P = f(t) be the population of the United States, in millions, t years after January…

A: We have to explain each mathematical statement into practice meaning.

Q: Y=t-2√√x + X Find domin and ringe

A: In this question, we want to know the domain and range of the given function.

Q: Sketch the graph indicating maxima, minima, asy 4-x³ function: f(x) = x3

A: Given: f(x)=4-x3x3

Q: (d) f(x)=√√x-8 (e) h(x)=√x+2

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Q: Consider the following function. Function f(x) = 8x4 - 6x³ - 165x² - 37x + 60 (a) Verify the given…

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Q: Consider the function below. ex f(x): 8 + ex (a) Find the vertical asymptote(s). (Enter your answers…

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Q: Find the derivative of the function. y=-5e-4x+1 dx 11

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Q: 7,000e0.1x dx   Find a substitution to rewrite the integrand as 70,000eu du. u=     du =        dx…

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Q: √√3 Lett be a real number and let P (1/1-4/3) 2 2 (a) Find the values of cost, and tant, and then…

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Q: given the following equation: 36y^2-4x^2=144.  a) determine if the function is an ellipses or a…

A: This question can be solved using the concept of conic section.

Q: 79 J ·S= sen7⁹ (x) dx. When applying variable change u-cos(x) 39 ○ a) J = [ (1 − u²) 3⁰ du Ob) J=…

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Q: 2. Find y' if y = 7* (log4 x)⁹.

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Q: y = x4 - 8x² + 8

A: Here we have to sketch the function y=x4-8x2+8 ............................................ (1)…

Q: 2 [[ (2a³y+9y³)d.A., D is the region bounded by y = x and y = 2√x. 3 33522 1050 1996 5 4811 None of…

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Q: Consider the function below. (If an answer does not exist, enter DNE.) C(x) = x¹/5(x + 6) (a) Find…

A: Let's solve.

Q: Find lim h-0 f(8+h)-f(8) h if f(x)=x² +9.

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Q: Find the exact length of the curve. y = 5 + cosh (2x), 0≤x≤ 7

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Q: 4) Find equations for the planes: b. The plane through (1.–1,3) parallel to the plane 3x+y+z=7

A: Given problem:- Find equations for the planes:   b. The plane through (1.-1,3) parallel to the plane…

Q: X Given that f'(x) x² +6 find F'(x) if F(x) = f(g(x)). F'(x) = = and g(x) = √3x – 4,

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Q: The graph of a function f is given below. JW y = f(x) X

A: from left graph of f(X) is increasing , f'(x) > 0  after that slope of line is steeper ,…

Q: Graph the rational function. -2x+2 -x+4 Start by drawing the vertical and horizontal asymptotes.…

A: This is a problem related to graph function. Based on the general formula and concept we will answer…

Q: Verify Property 2 of the definition of a probability density function over the given interval. f(x)…

A: Given problem:- Verify Property 2 of the definition of a probability density function over the given…

Q: Find the equation the tangent line and normal line to the graph of f(x) = √x at x = 4. Graph the…

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Q: Use any method to determine whether the series converges or diverges. (k!) 8 (8k)! k=0 O The series…

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Q: Solve for x: |x+5| < |X-71

A: Follow the procedure given below.

Q: d. The plane through P,(2,4,5) perpendicular to the line x=5+t y=1+3t .

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Q: Given the function z=f(x,y)=2y³ −6xy − 3x² +2, find the following: a) Vf= b) Find all of the…

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Q: Ive the given differential equation using two (2) methods. (x² + 6y2) dx - 4xydy = 0; if x = 1, y =…

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Q: Annual sales of bottled water in the U.S. in the period 2000-2010 can be approximated by the…

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Q: Evaluate fea cos(2x) dx

A: We have to above integration

Q: For each function, determine whether it is a polynomial function. Function (a) v(x)=3x² +0.6x4 (b)…

A: polynomial can have constants (like 4), variables (like x or y) and exponents (like the 2 in y2),…

Q: Evaluate x³ + €

A: On solving this we will get

Q: A group of 10 wolves are introduced to a national park. The park can support 100 wolves. After 1…

A: By making differential equation

Q: angle betw 2. Determine whether the vectors a and b are parallel, orthogonal or neither for the…

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Q: Prove that sech-¹(x) = In (¹+√¹-x²) X

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Q: Solve the given equation for x. 75x-5 = 31

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Q: ind the indicated function and write its domain 8) p(x) = x² + 6x, q(x)=√√1-x, (x) = ?

A: We have to determine domain

Q: B2. Find the integrating factor by inspection then solve.  y(y2 + 1)dx + x(y2 - 1)dy = 0

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Q: 4. Find an equation for the plane through (1, 3, 4), with normal vector . 5. Find parametric…

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Q: Determine the center and radius of a circle given that its equation is (x + 10)² + (y − 4)² = 4 Use…

A: Explanation of the answer is as follows

Q: Consider the improper integral and the propositions dx J = = 6of foo x² + 3 1- The integral J…

A: Find out the correct statement.

Q: Find the integrating factor by inspection then solve.  y(3xy + 1)dx - xdy = 0

A: y(3xy+1)dx-xdy=0

Q: /sin-¹ (√x) dx tegral.

A: Let I=∫sin-1x  dx

Q: 1. Find when y = In (-²). dx Express your answer in a single fraction.

A: The given function,     y=lnx5-2x

Q: Find the volume generated by revolving the given plane area about the given line using the washer…

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Q: A rectangular zone measuring 12 miles by 16 miles contains five buildings. What is the maximum…

A: Concept: We have a rectangular zone that measures 16miles and 12 miles Let the five buildings in the…

Q: Describe the difference between a discontinuity that is removable and a discontinuity that is…

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Q: A golf ball is launched into the air with an upward velocity of 81 feet per second. The height of…

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Q: 3. Find the integrating factor e∫Pdx then find the general solution. 2(y - 4x2)dx + xdy = 0

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Q: The population of a small country by year is shown in the table below. Year 1955 1960 Population…

A: If population of a city x in 1950 and y in 1960 then absolute change of population=(y-x)  As per our…