1. Carbon 14 is a common form of carbon which decays over time. The initial amount of carbon 14 contained in a preserved plant is 10 micrograms. If there is currently one microgram of carbon 14 remaining in the preserved plant. Approximately when did the plant die?

Q: f(x, y, z) = 2 ≤ x ≤ 10,0 ≤ y ≤ 4,0 ≤ z ≤4

A:

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A:

Q: Test and k=/ each name K+ k³+1 of all the tests following. you for use. Conver

A:

Q: Sketch a graph of a continuous function f with the following properties: (i) f(x)=0 for x = 0 (ii)…

A:

Q: 12. How long will it take an investment that earns 17.6% annual interest, compounded continuously to…

A: Above quedtion is solved. Only one question is solved. Solving more than 1 question is against the…

Q: Evaluate [ f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

A:

Q: 1. Consider the vectors ā=27 +47-6k, b=-37+k, and a = 37-2k. [K/U] [1] a) Find the magnitude of the…

A:

Q: Express the rule in function notation. (for example the rule “square, the subtract 5”is expressed as…

A:

Q: h. Use the second derivative to identify intervals where f(x) is concave up. (-0,3) X i. Use the…

A:

Q: A cylindrical can without a top is made to contain 10,000 cubic cm of liquid. Find the dimensions…

A:

Q: Evaluate the indefinite integral. 4 (t + 4)³ dt + C

A: Topic = Integration

Q: 5 (x²-4)

A:

Q: Consider the rational function f(x) = x²-x-6 x²+3x (i) Factorise the numerator and denominator. (ii)…

A: As per guidelines, we must answer only three of the subparts of a question given. So, I answer the…

Q: у 7. y' +²√y = 0, y(1) = 0 - x

A:

Q: Let f(x) = x¹ - 50x² 3 (a) Use the definition of a derivative or the derivative rules to find ƒ'(x)…

A: "since you have posted a question with multiple subparts,we will solve first three subparts for…

Q: ¹ // x² + y² + 2² dV, where E is the ball: x² + y² + z² ≤ 16. Use spherical coordinates to evaluate…

A:

Q: Two cars are moving towards an intersection. One car is 190 meters north of the intersection and…

A:

Q: 1. sin x sin 2x + cos x cos 2x = COS X

A:

Q: Use the graph of f (x): = Enter the exact answer. 1/1/00 below to find a number & such that |ƒ (x) -…

A: The objective is to find the value of delta.

Q: Let R be the region enclosed between the curves r²=y-1 and y=5. Sketch R and find its area.

A: The region R is enclosed between the curves x2=y-1 and y=5 we have to sketch the region R and find…

Q: Find the the maclaurin following: four Series nonzero terms of the for each

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

Q: 8. What is the domain and range of the following relation? y=x²-2x-3 y 5 8 X

A:

Q: f(x) = 3 x³ Y g (x) w X -

A: Concept: Area between the two curves: The definite integral of one function, such as f(x), minus the…

Q: e) 3 (12x²-108) 2 x + x - 12

A:

Q: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

A:

Q: The graph of f(x) is shown (see figure). 2X f(x) = (a) Find the following limits. L = lim f(x) = V…

A: According to guidelines, we must answer only three of the multiple subparts given. So, I answered…

Q: Consider the following function. f(x) = (x-8)ex (a) Find the critical numbers of f. (Enter your…

A:

Q: 1. Which of the following functions grows the fastest as x goes to infinity? O 2x О 3x O Ox20 ex

A:

Q: Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the…

A:

Q: Which function has Maclaurin series (-1)"2""? n:o OAI OB 8. 2/7/2 Oc O D. TIZE D.E. 2

A: The given series: ∑n=0∞-1n2nxn

Q: d) 2 x +8x + 15 2 x+5x+6

A:

Q: Part A The population p, in thousands of bacterial colonies on a kitchen bench can be modelled by…

A:

Q: Question 1 Find lim f(x) given the graph of f(x) shown below. x-5 +++ -10-9-8-7- Y 3 4 5 6 7 9 10 x

A:

Q: The surfaces p= 3 and 5, p = 100° and 130°, and z = 3 and 4.5 identify a closed surface. (a) Find…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the exact average value fare of f(2)=√16-2² between 0 and 4, then find an exact number e in…

A:

Q: a) 0 1:3 x dx -3√√9-x² V 2

A: The objective is to evaluate the integral.

Q: Solve the differential equation of dx (A) In y = c Inx

A: Given: dydx=ylnx

Q: Solve x (az + √2) dx y (az + √2) sin (ay²) dy + (az − √2) dz = 0 4√/2ln |az + √2 = C 4√/2ln|az +…

A:

Q: dv/du = (u — v)² — 2(u - v) - 2.

A: Here, the given DE is: dvdu=(u-v)2-2(u-v)-2...(1) Substitute u-v=p differentiating it with respect…

Q: The demand for a certain product is given by the function D(q)= −2.1q+350 where q is the quantity in…

A: Given, The demand for a certain product is given by the function D(q)= −2.1q+350 where q is the…

Q: Find the direction vector of the line which is the intersection of the planes x + y + z = 1 and…

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

Q: 10. Evaluate f(x) = 10-4x for f(3). a) 23 b) 2 c) 22 d) -2

A:

Q: dx b) √ COS √x cos(1-√√x) 818

A:

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A:

Q: Use polar coordinates to evaluate the double integral. 1 1 + x² + y² where R is the sector in the…

A: Given data:- the double integral, ∫∫R11+x2+y2 dA R is the region y=0, y=x, and  x2+y2=4

Q: d) Explain what happens to p't) for t greater than the value you found in part c. Give one reason…

A: p'(t) for t greater than the value of 10 becomes stable and reaches to a threshold value

Q: 2. Consider the parallelogram ABCD where A(0,1,2), B(1,2,3), and C(0,3,5). [2] a) Find the…

A:

Q: 5. 6. 7. 8. √√x-1 lim- x-1 x-1 x³-x²-x+10 lim X4-2 x²+3x+2 2x²-x-3 lim x-1x³ + 2x² + 6x +5 lim…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 10. Find the area bounded by the curve x = y² + 2y and the line x = 3.

A: Area Bounded by the Curves : If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y), then…

Q: Determine the limits of the following Limit/ 1-c05 (22²) Ayo sinx

A: