2. A basketball is being filled with air at a rate of 6 in /sec. (You can assume the basketball is a perfect sphere). How fast is the diameter of the basketball increasing when the radius is 1 in?

Q: 4e2x S sin(e²x) dx

A:

Q: Solve the initial-value problem. (Use t as your independent variable.) P' = 7P(1 − P),      P(0) =…

A:

Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t+ 32) sin(t)dt

A: We nee to evaluate ∫t3-4t2+5t+32 sin(t) dt

Q: A child enters a carousel that takes one minute to revolve once around. The child enters at the…

A: Given problem:- A child enters a carousel that takes one minute to revolve once around. The child…

Q: = 0.3t centimeters per minute 2. The depth of the water in a tank is changing at a rate of r(t) O,…

A:

Q: 4. Find the equation/s of the normal line of slope 2 to the ellipse x² + 2y² = 3. 5. At what point…

A:

Q: I am stuck on the maximum and minimum values of y and corresponding x.  Will you please assist on…

A:

Q: 1 (2m-3)√4m (m-3) dm

A: Given

Q: noon and 2 pm the population triples, at what time should the population become 100 times what it…

A:

Q: Find the equation of a circle whose center is at the intersection between the lines 3x - y = 2 and…

A: The standard form of the equation of a circle is x-h2+y-k2=r2 where (h, k) is the center of the…

Q: (a) Find (in terms of m) lim f(x) z--1¹ Limit= (b) Find (in terms of m) _lim_ f(x) Limit= (c) Find…

A:

Q: Evaluate [[r'dr de over the area bounded between the circler = 2 cos@ and r= 4 cos -41π/2 O -43π/2 O…

A:

Q: Determine whether the given function is even, or odd, or neither. One period is defined for the…

A: We have to find if the function is even or odd.

Q: A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from…

A: A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from…

Q: Q2: dy du (A) Show that if y=csc(u), then -csc(u) cot(u) dx dx

A:

Q: Find the arc length of the curve x = Length = -2y³/2 from y = 0 to y = 10.

A: See the details solution in below

Q: Use the functions f(x) = x + 4 and g(x) = 2x³ to find g-¹ o f-¹

A:

Q: (B): Find the integration by using substitution method √x√2x - 1 dx

A:

Q: (B) let y = 3sin5x-2cos5x show that y + 25y = 0

A: Given :y=3sin5x-2cos5x    To prove : y''+25y=0

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+ 32)sin(t)dt

A:

Q: Find the area of the surface obtained by rotating the curve from x = 0 to x = 5 about the x-axis.…

A:

Q: Determine the arc length of the curve formed by the polar equation r = 4 cos 0 - 4. 2T 2п 2√/2 √1 -…

A:

Q: find the given general differential solution, using homogeneous equations with constant…

A:

Q: F(x, y) = 6xyi + 3y²j is a conservative vector field.

A: Given :F(x,y)=6xyi+3y2j

Q: Find a power series representation for the function. f(x) = x2 tan-1(x3) f(x) = Σ n = 0 Determine…

A:

Q: √tanx secox dx

A: We know that integration of xn is xn+1/n+1.   Here i attached the solution of this question.

Q: find the given differential solution, using homogeneous equations with constant coefficients.…

A: Solution: The objective is to find the general solution of the given homogeneous differential…

Q: Consider the function f(x) = 4sin(pi/3(x-2) + 8  what is the maximum and minimum y values and their…

A:

Q: 1 Use technology to help you sketch the graph of each function for 0≤x≤ 2. a y sinx by=2 sinx c y=3…

A:

Q: C 10 A 3 2- 1 1 2 3 4 To find the blue shaded area above, we would calculate: [1(x)d f(x)dx = area…

A: As shown in diagram, lower limit is 1 and upper limit is 2, Therefore a=1b=2

Q: 1/0 1,0 -3 -6 Note: Enter 'DNE' if the limit does not exist or is not defined. I

A: \

Q: Find the tangential and normal components of the acceleration vector. r(t) = 4(3tt³)i + 12t²j at X…

A:

Q: Find the flow of the vector field F(x, y, z) = zi + yj + xk through the unit sphere x² + y² + z² = 1…

A:

Q: Is it possible to get the area 2 3 between y² = 3x and y = x³, using a. vertical strips b.…

A:

Q: Q5: (A): Finding a curve whose slope at the point (x, y)is 3x² if the curve is required to pass…

A:

Q: Consider the function f(2)=2 sin ((z-3)) +6. State the amplitude A, period P, and midline. State the…

A: This question can be solved using the concept of general equation of sine curve.

Q: (3+h)¹-81 The following limit limh→0 h represents the derivative of some function f at some number…

A:

Q: What value of x is paired to y=15 using the function f(x) = 2x²-3x+1? none of the choices O-2 3 2

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

Q: 7. sech²(Inx) dx X

A: Let's solve given integral.

Q: Suppose that P₂(x) = a + bx + cx² is the second degree Taylor polynomial for the function f about x…

A:

Q: H.W find the first four terms of the binomial series for the functions:- 4-(1+¹)¹/² 5-(1+x)*…

A:

Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: 1. Find the limit, if it exists. If the limit does not exist, explain why. 8x³+2x+1+x+2 (b) lim 5x +…

A: Solution: The objective is to find the given limit

Q: What is the general formula for the nth term of the sequence –4, 1, 8, 17, 28, ...?

A: To determine the general formula for the nth term of the following sequence.  –4, 1, 8, 17, 28, ...…

Q: Find all solutions of the equation in the interval [0, 27). 2 cos 0+1=0 Write your answer in radians…

A: Given:   2cosθ+1=0   2cosθ+1-1=0-1             {subtract 1 from both sides}   2cosθ=-1   2cosθ2=-12…

Q: 4. Evaluate the double integral: L Lates y¹/3 x² 27 +1 (Hint: Change the order of integration to dy…

A:

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+32)sin(t)dt

A:

Q: sec¹ x dx

A:

Q: Let D be the region in the first octant enclosed by the two spheres x² + y² + z² = 4 and x² + y² +…

A:

Q: 1. find the given differential solution, using homogeneous equations with constant coefficients.…

A: