use the appropriate limit laws and theorems to determine the limit of the sequence or show that it diverges.

Q: A man starts walking north at 3 ft/s from a point P. Five minutes later a woman starts walking south…

A:

Q: For a plane curve r(t) = (x(t), y(t)), k(t) : k(4) = = |x'(t)y"(t) — x"(t)y' (t)| (x'(t)² +…

A:

Q: If f(x) da = 16 and ¹ Answer: fr f(x) dx = 3.1, find f(x) dx.

A: We know that the formula int_a^b f(x) dx=-int_b^a f(x) dx

Q: Determine the area of a triangle having the following measurements. C = 82° 34', a = 11.0, and b =…

A: Here the measurements  are given for a triangle . Now we have to find it's area.

Q: f(x) ²-7 2 6 X if 0 < x <b if b <x (9) Determine a value of b for which f is continuous at b. (b) Is…

A: We have to find whether the function is continuous at the point x=b or not. A function f(x)…

Q: The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas. 1. f* f…

A:

Q: The graphs of f(x) = x²-3x - 4 and g(x) = -2x - 2 intersect at the point (-1,0). The (acute) angle…

A:

Q: Use a change of variables to find the area of the region R enclosed by the lines x + y = 4, x + y =…

A: To find the area of the region R enclosed by the given lines, we can use a change of variables and…

Q: B IUL 1:3 41) The bacteria in a 8-liter container double every 2 minutes. After 56 minutes the…

A:

Q: 37. a. Show that the function is a solution of the differential equation b. Show that f(x) = eª .…

A:

Q: 3. Evaluate each of the following limits, if they exist. lim (1+1)* [A5] a) x²-√√x b) lim x+1 √x-1…

A: To evaluate the limit first check whether the given equation is in determinate form or indeterminate…

Q: Let the vector v have an initial point at (4, 7) and a terminal point at (-2, 6). Plot the vector v…

A:

Q: Use the graph of the rational function f(x) to complete the statement. As x 27, f(x)→ -10 OO -2 +∞ 0…

A:

Q: Suppose that we don't have a formula for g(x) but we know that g(2) = -4 and g'(x)=√√x² + 5 for all…

A:

Q: Consider the following. C dt = Let t = 7 tan(0) and determine the t = 0-0 = = 7 t = 70 = 0 dt 49 +…

A:

Q: Consider the general alternating harmonic series: Determine whether the series converges absolutely,…

A: The general alternating harmonic  series:-

Q: Trace the evaluation of the following expressions, and give their resulting values. Make sure to…

A: To trace the evaluation of the following expressions, and to give  their resulting values. (i)…

Q: Find the first partial derivatives of the function. 4 f(x, y) = x² + 7xy5 X fx(x, y) = fy(x, y) =

A: Given f(x, y) = x4 + 7xy5

Q: Write a polar equation of a conic with the focus at the origin and the given data. eccentricity y…

A: Given: Conic is ellipse, eccentricity = 14, directrix y=8 To find: Polar equation of ellipse with…

Q: Find the total mass of a 1 meter rod whose linear density 17 function is p(x) kg/m for 0 ≤ x ≤ 1 (x…

A:

Q: Solve the trigonometric equation for all values 0 < x < 5. tan ㅠ -X- 3 - √3=0

A:

Q: Determine the value of k so that ū = [-5, k, 3] and = [1,2,- 7] are orthogonal.

A:

Q: Find the magnitude of the vector. Given answers in simplest radical form for magnitude. p =

A:

Q: ππ|2 ff sin(2x)cos(3y)dx dy 00

A: Use the double integral separate the variable

Q: 6. Consider the following graph of the function f(x) = cos(x). Draw on top of the graph to indicate…

A: Here we have given a function: f(x)=cosx. a) The limit that will compute the exact area represented…

Q: QUESTION 4 Determine the number of triangles with the given parts. b= 10, a = 65°, y = 132° 0 1 2…

A:

Q: Use the limit comparison test to determine if the series converges of [ 30².6 n-o O Converges O…

A:

Q: Construct a problem where the derivative of a point on a graph is equal to 1. It cannot be a linear…

A: To construct a problem where the derivative of a point on a graph is equal to 1.

Q: Solve the first-order linear differential equation. (Use C for any needed constant.) y' 3y = e-3. y…

A:

Q: Find the volume of the solid formed by rotating the region enclosed by y=e¹ +3, y=0, x=0, x=0.8…

A: Consider the given function y=ex+3, y=0, x=0, x=0.8The volume about x axis is evaluated  as…

Q: 11. According to a formula discovered by the French physician Poiceulle, the velocity (in cm/sec) of…

A: According to a formula discovered by the French physician Poiceulle,  the velocity (in cm/sec) of…

Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. 4 √x - 4 f(x) lim x…

A:

Q: Let R be the region bounded by the graphs of x=y^2-4 and 1/8 y^4-y^2+2 as shown below. Calculate the…

A: x=y2-4 and x=18y4-y2+2

Q: Find the following for p =, q =, and r =. Find -2p - r

A: Given that,    p = -7, -6  q= -1, -11, r= 0,9 we have to find the value of -2p-r.

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate (in…

A:

Q: A solid is formed by rotating the region in the xy-plane bounded by the curves y = 7x², x = 1 and…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: 21. f(x) = ln (5 - x)

A: 11-u = ∑n=0∞ un = 1+u+u2+u3 +...

Q: A hot object cools down according to Newton's Law so that thours after the start, the rate that heat…

A: The rate that heat leaves are 26e-t3

Q: 7. For the function f(x) = xe-, find the intervals on which the function is concave up and concave…

A:

Q: Find the value of the constant a such that the function f(x) is continuous for all values of x. 4…

A: fx=ax+4xx&lt;2ax2x≥2

Q: 14. let F(x) = x O find the values of x where f'(x) = 5 X+6 Give exact anwers (not decimal…

A:

Q: Let the vector v have an initial point at (-3,0) and a terminal point at (-4, –3). Determine the…

A: The initial point of the vector is x1, y1 = -3, 0 The terminal point of the vector is x2, y2 = -4,-3…

Q: Calculate (t) when k(t) = = r(t) = (3t-¹,-1,5t)

A:

Q: Let G be the region in the plane the curve ▷ and x=1. ▷ bounded by y= ex and the lines y=-x+1 a)…

A: The given curves are: y=e-x,     y=-x+1     and    x=1

Q: Find the absolute value of the complex number 1 + 2i.

A: We need to find the absolute of given complex number.

Q: Consider the following. 7 dt 1²= V 49 + t² Let t = 7 tan(0) and determine the following. dt = t =…

A:

Q: (c) Now estimate the area under the graph of f using eight approximating rectangles and taking the…

A:

Q: For the curve given by Find the unit tangent T(t) = ( Find the unit normal N(t) = ( Find the…

A:

Q: Differentiate f(x) = cos - ¹ ( f'(x) =

A: NOTE: Refresh your page if you can't see any equations. . take derivative apply chain rule:…

Q: Given: (x is number of items) Demand function: d(x) 5120 √x Supply function: s(x) = 5√√x Find the…

A: