(1) Use the definition to prove that if x₂ → 2 then (2x, +1)/x → 5/2.

Q: You want to buy a $243,000 home. You plan to pay 10% as a down payment, and take out a loan with a…

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Q: □ on show that f(x)= 3x is inte the integralble definition. I043 uning [0,4]

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A: To find out the equation of line.

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Q: explian how to get the domain, vertical asymptote, and end behavior of  h(x)=-log(3x-4)+6

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Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

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Q: y = √√2x-5, y = 0, x=4

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A: We have to find the conservative vector field.

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Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A: Given problem:- The population of mosquitoes in a certain area increases at a rate proportional to…

Q: Find the second order derivation for y = e-3x².

A: d2dx2e-3x2

Q: y² = 8x,x=2, AOR = Y AXIS

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Q: A company's revenue from selling x units of an item is given as R = 1000x - x² dollars. If sales are…

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Q: 6 4 If f(x) = 4+ + I I find f'(x).

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Q: If w=f(p, q, r), where p-z2-y², q=y²-22, and r = 22-2², show that 1 Ow x 8x + 1 8w у ду + 18w z Əz…

A: Given w=f(p,q,r)and p=x2-y2,   q=y2-z2 and r=z2-x2

Q: Find an equation of the tangent plane to the surface g(x, y)=x²-y² at the point (7, 4, 33). O…

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Q: Calculate the following two indefinite integrals. Thank you. (6e^(2x)-5x^(3)+(4/x)+3)dx

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Q: FIND THE DERIVATIVE OF THE FOLLOWING FUNCTIONS. g(x)=xnx

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Q: Find all real zeros of the function. f(x) = -5x (1²-16)(x-2) If there is more than one answer,…

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Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find f'(1). Note: Your answer (if it's not an integer)…

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Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

A: We want to find the area of region bounded between the given curves

Q: The population density of a city is approximated by the model f(x, y) = 2000e-0.01(x² + y²), x² + y²…

A: This is a problem related to double integration. Please follow the general procedure given below.

Q: Find the derivative of f(x) = = 30 6/4x+1 Enclose numerators and denominators in parentheses. For…

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Q: Let f g and h be the functions defined below i. 11. f(x) = 5¹ = 10x₁ (²² = 4) g(x) = log5 h(x) = 6 x…

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Q: - The equation of the sphere centered at C(h, k, l) and radius r is given by (x − h)² + (y − k)² +…

A: The given sphere equation x2+y2+z2-4x+2y+6z-11=0

Q: 9 (4) Giver Sifon dx = 37 g(x) dx = 16 So Find S (2 f5r1 + 3 ger)) f(x) dx and

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Q: The area of the region inside the circle r = 6 cos 0 and outside the cardioid r = 2(1 + cos), a > 0…

A: Given: the circle r =6 cos θ and the cardioid r=2(1+cosθ )

Q: Ow Find using the appropriate Chain Rule for w=y³-5x²y where x = es and y = e, and evaluate the…

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Q: A homeowner wants to enclose three adjacent rectangular pens of equal size, as in the following…

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Q: R. -6 -2 7 π/2 ett 4 2 i -2 2 π/2 4 ett 2 4 O 2 4 T/2 8 6 4 2 π/2 4 2 D 2 2 P 50 4 8

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Q: Find all x-intercepts and y-intercepts of the graph of the function. 2 f(x)=1³-1²-9x+9 If there is…

A: We will solve.

Q: Graph the following function, showing all asymptotes and relative extreme points. 16 O TV.W.N f(x) =…

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Q: Evaluate the function at the given values of the independent variable. Simplify the results. f(x) =…

A: The given function, fx=6x-1

Q: QUESTION 2 a) Evaluate the area of a region that lies inside the circle x² + (y-3)2 = 9, but outside…

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Q: Sketch the graph of the equation by point plotting. y = 5-x² -3 X y -2 0 2 3

A: Sketch the graph of the equation by point plotting

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Q: Find all values of c such that fis continuous on (-∞,). C= 7-2², a se - ذکر (smaller value) (larger…

A: Given query is to find the value of c so the function is continuous for the provided interval.

Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

A: Find the volume of the solid bounded by the curve Z=ln(x2+y2)z=0x2+y2≥1x2+y2≤9

Q: y = ³/2, y = 8, x = 0

A: answer is in next step. please give a like .

Q: At the beginning of an experiment, a scientist has 160 grams of radioactive goo. After 90 minutes,…

A: topic- exponential function

Q: Sketch the region R and evaluate the iterated integral IT x²y² dx dy y 10 8 6 2 y 10 8 00 6 4 2 [[…

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Q: Consider the function. X 10/17 - 12/24 5 Find Duf(7, 1), where u = cos(0)i + sin(0)j. f(x, y) = 8

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Q: Find the equation of the tangent line to the graph of the function f(2)=sin(7√) at the point (²,0).…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  so we can take

Q: Consider the function g(x) =−4 log (−1/3 (x + 2)) + 1. a) Describe, in order and with detail, the…

A: We will use concepts of translation , dilation and reflection.

Q: Find the derivative of f (y) 30% In(y) Enclose arguments of functions, numerators, and denominators…

A: To find the derivative of the given function.

Q: (a) cos(8): = √2 2

A: answer is in next step. please give a like .

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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