Let S be the hemisphere x² + y² + z² = 4, with z ≥ 0. Evaluate the surface integral JS₂ S z² ds: = 64pi/3

Q: The average value of v(x) equals 2 for 1 ≤ x ≤ 3, and equals 6 for 3 ≤ x ≤ 11. Find 11 ["v v(x)dx 72…

A: The average value of  equals 2 for , and equals 6 for .To find .

Q: a) The rectangles in the graph below illustrate a The value of this Riemann sum is left endpoint…

A: given function

Q: If xy + y² = 1 find the value of dy / dx² at the point (0-1)

A:

Q: Evaluate the integral by interpreting it in terms of areas. 1₁ ( 2 + √ 49-x²) dx

A: simplify the integral

Q: Question 4 Suppose an> 0 for n≥1 and lim wan > 1 n→∞ n=1 an? What can you conclude regarding The…

A:

Q: please shed some light on how you got the critical numbe

A: So, f'(x)=0 gives us

Q: PLEASE PLEASE HELP, The x y-coordinate plane is given. The curve starts at the point (1, 7), goes…

A:

Q: Find all solutions of the equation. +√√2=0 6) 2 cos x + 1

A:

Q: Find the exact coordinates of the centroid of the following semicircular plate. Show all steps…

A:

Q: (a) Find the number a such that the line x = a bisects the area under the curve below. 1≤ x ≤4 a =…

A: The region under the curve,  To find the value of b such that the line bisects the area

Q: Exercise 4. Prove the following claims. (i) Let f: R² →→ R be defined as f(x, y) := { 3 xy x² + y²…

A: The condition of function in R2 must fullfill in order to be continuous isf(a, b) = lim (x, y) ->…

Q: nd the general solution of 2 = Sin x

A: y' = sin2x

Q: Multiply both sides by (x² + 1)² and combine like terms. x² + 6x + 1 = (Ax + B)(x² + 1) + Cx + D =…

A: The given equation

Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

A:

Q: * Find the general Solution of :- - dy хе dxx New 1=Y, NOVIR VO

A: The given equation is; dy/dx = xex

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for ƒ(x) = √√x + 16 on the…

A: To verify that the hypotheses of the Mean-Value Theorem are satisfiedfor  on the interval , and to…

Q: A 4.6 ft tall man is walking away from a 28 ft tall lamp post. If he is walking at a rate of 4 ft/s,…

A:

Q: Calculus 1

A: z=2x2+xyx=cost, y=2sint

Q: f(x) || 1 x² + 1

A:

Q: Let G be a function whose derivative is shown below. Assume the domains of G and G'are 0 ≤ x ≤ 12. 8…

A: We have given a graph of G'(x) in the interval . We have to find the value of G( 6) and coordinates…

Q: pлd¹ The rate of flow, Q of a fluid through a pipe of diameter, d and a length, L'is given by Q…

A:

Q: Given. [₁3 Evaluate. 3x√x² +9dx = 10√10 - 27 [₁³ 3u√u² +9du

A:

Q: Find all critical points of the function f(x) = 2x³ - 14x² + 11x on the interval [0,7). (Use…

A:

Q: Solve a Consumers' or Producers' Surplus Problem. A sports watch has a price-demand equation given…

A: The objective of this question is to calculate the consumers' surplus and the producers' surplus for…

Q: Use the Ratio Test to determine whether onvergent conditionally, or divergent. n=1 (−77)” n! is…

A:

Q: 1 Evalvate the following integrals (use method of integration by parts): 2 (₁) S (sinth) ² dre

A:

Q: Evaluate the integral: /9 - x² = dx (A) Which trig substitution is correct for this integral? 0x = 9…

A: Given indefinite integral is

Q: Find f such that f'(x) = f(x) = √x¹ f(1) = 13. ***

A:

Q: Consider the function f(x) = 2sin(x²) on the interval 0 ≤ x ≤ 3. (a) Find the exact value in the…

A:

Q: The amount of carbon-14 present in animal bones t years after the animal's death is given by P(t) =…

A: The amount of carbon-14 present in animal bones t years after the animal's death is given…

Q: The graph of a derivative f' (x) is shown in the figure below. LA 1 2 3 4 5 6 -3 Enter the exact…

A:

Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and for the…

A:

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: , n=5a=0, b=4

Q: f(t) = 1-2t 1 + 2t

A:

Q: The graph of the first derivative of p(x) is shown in the graph below. Use the graph to answer the…

A: The graph of the derivative function is given.The aim is to find the interval at which the function…

Q: 9 √x Find all critical numbers of the function f(x) = 7√x- If there are multiple critical numbers,…

A:

Q: Tutorial Exercise Evaluate the integral by interpreting it in terms of areas. f (x-14) de Part 1 of…

A:

Q: Evaluate the integral: - 20 √2²√2² + 64 x²₁ dx (A) Which trig substitution is correct for this…

A: To evaluate the following integral.

Q: * Find the general Solution of dy dx = 4. x² ln x

A: The given differential equation is

Q: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by fat x = a. 1 f(x) = -— , a=3 X…

A:

Q: Find the local maximum of f(x,y) = xy(1-x-y) Find the critical point(s) and check the value of D = f…

A: given function

Q: Find all relative extrema. Use the Second-Derivative Test where applicable. (If an answer does not…

A: To find all relative exrema of the following function.

Q: olve the following integration:- 2 x² + 3 x(x-2)(x-6) ² dx

A:

Q: 13. If lim f(x) = lim g(x) = + ∞o and f'(x) = 1 and g'(x) = ex, what is lim 818 x480 x → ∞ g(x) A.…

A:

Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f(x) = cos(x) on the interval [3π 5π…

A: 1) f(x) is continuous on [a,b],2) f(x) is differentiable on (a,b), and3) f(a) = f(b)then there…

Q: Find the general Solution of: dy dx XsinX

A: The differential equation given is

Q: (a) Determine whether the given integral is improper or not. You need to explain why it is either…

A:

Q: use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A:

Q: Use substitution to find the Taylor series at x = 0 of the function In (1+5x9). What is the general…

A:

Q: Find the Maclaurin series for the given function. 3e-x

A: A Maclaurin series is given by f(x)=∑k=0∞f(k)(a)k!xk