Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = ½, y = 0, x = 2, x = 9; about y = -1

Q: 1. Verify the following trigonometric identities. (a) sin x tan x = secx- cos x sinx sinx - Cos X…

A:

Q: Evaluate the integral. -4e - 6 e2x + 3x + 2 dx +C

A: Final answer:∫e2x+3ex+2−4ex−6​dx=2ln(ex+1)+ln(ex+2)−3x+CExplanation:Step 1:Given integral:…

Q: Problem #4: The inverse Laplace transform f(t) = £¯¹{F(s)} of the function e-³(8s-7) F(s) +16 is of…

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Q: Answer the following questions about the function whose derivative is f'(x)=3x(x-5). a. What are the…

A: a)  A . X = 0 , 5  b) A. Increasing on intervals  (−∞,0) U (5,∞) and decreasing on (0,5) c)  llocal…

Q: x+1, x0 Can also be displayed as: ) = [ x+1 when x 0]

A: find the continuity of the function

Q: Find the interval of convergence of the power series, where k is a positive integer. kkl x/x Σ) n =…

A: Hence the final answer is : The interval of convergence is (−k,k)Explanation:To find the interval of…

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves abo the…

A: The objective of this problem is to find the volume of the solid obtained by rotating the region…

Q: After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world…

A: The objective of the question is to find the projected annual average population growth rate in 2020…

Q: 2πT Find the vector given that its magnitude is 6 and it makes an angle with the positive x-axis. 3…

A: Therefore,v=−3i^+33​j^​Explanation:Step 1: Let v=vx​i^+vy​j^​ a vector that makes an angle θ with…

Q: Find the volume of the solid beneath the surface z=4-y2 on the region bounded between the curves y =…

A: The objective of this question is to find the volume of the solid beneath the surface z=4-y^2 on the…

Q: Explain how to solve this question with steps.

A: All steps given below.  Explanation:

Q: 3. A) www Find the circulation of F = -yi + x²j + zk around the oriented boundary of the part of the…

A: The objective of the question is two-fold. First, we need to find the circulation of the given…

Q: Identify the inflection points and local maxima and minima of the function graphed to the right.…

A: The inflection point is at x = 2.Local maximum of (8/3) at x = -1.Local minimum of (-100/3) at x =…

Q: A particle moving in the xy-plane has a position vector (est, √) for t≥0. The acceleration vector of…

A:

Q: Find the exact value of each of the following under the given conditions. 3 œ lies in quadrant II,…

A: Answer:  a) 10021−247​​b) 100−72−77​​c) 72+77​−21+247​​Explanation:Step 1:Step 2:

Q: How do I find all that is being asked for?

A: (a)The maximum height reached by the ball= 100 ft. (b) on the ball's way up, when it is 96 ft above…

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: ∫(12t3−72t−3)dt=3t4+36t−2+CThis is the required answer.Explanation:Step…

Q: All graphs/sketches must be accompanied by all algebraic work as per the Curve Sketching Algorithm…

A: all answers are explained below in detail. Explanation:

Q: Use Green's theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

A: I=∫CF⋅drI=∫C(3+ex2)dx+(tan−1⁡(y)+3x2)dy

Q: Find the average rate of change for the function over the given interval. y=4x² between x=0 and x =…

A: The objective of this question is to find the average rate of change of the function y=4x^2 over the…

Q: Find the gradient of the tangent to S(t): = 5t +7 +2 at the point where t = −1.

A: The objective of this question is to find the gradient of the tangent to the function S(t) = 5t + 7…

Q: The graph to the right shows the first and second derivative of a function y = passes through the…

A: The given graph

Q: Sketch the graph of a differentiable function y = f(x) through the point (1,1) if f'(1) = 0 and…

A: Ans:Detailed answers in explanation please referAny confusion please ask in clarification will…

Q: Help

A: ​Slope of tangent line, mT​=−23​​Explanation:Step 1:​Parametric curve {x=2cos(t)y=3sin(t)​ at the…

Q: onsider the function f(x) = (3x-6) / (x+5) Find: (a) f increasing and decreasing (b) concave up…

A: The given function

Q: Evaluate the function. -18 X=1 If y = f(x), find f(1). 18 1 Y=2 -10 10

A: • f(x) = -x + 3• f(1) = 2Explanation:

Q: Use P(x) = -1x++ 4x³ to answer the questions. (a) Find the x- and y-intercepts. (If an answer does…

A: (a) The x-intercepts are:- (0, 0)- (4, 0)The y-intercept is (0, 0).(b)y→−∞ as x→+∞y→−∞ as…

Q: A calculator may not be used on the following questions. A particle moves in the xy-plane for >0 so…

A: Option a is correct i.e To the left and up Explanation:Step 1: Step 2:

Q: 5) Which of the following statements is ALWAYS TRUE? a) An absolute minimum must be a local minimum.…

A:

Q: What is the equation of the tangent to the curve of the function: (Question in the picture)

A: The objective of this question is to find the equation of the tangent line to the curve of the given…

Q: Write the expression as the sine, cosine, or tangent of an angle. Then find the exact value of the…

A:

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge.\int_(-\infty )^7…

A: The given integral is converges.  ∫−∞7​x2+91​dx=31​tan−1(37​)+6π​ Explanation:

Q: Match each of the following with the correct statement. A. The series is absolutely convergent. C.…

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: f(x)= x + 1, 0, x²+1, Can also be displayed as: *0 x+1 when x < 0, 0 when x = 0, x² + 1 when x ƒ(2)…

A:

Q: In one town the annual consumption, b, of beef (in pounds per person) can be estimated by b = 32…

A: The objective of the question is to find the t-intercept of the function b = 32 - 0.5t and interpret…

Q: 5

A: The required volume isV=2π(tan1−1)=3.5022Explanation:Given curves are:y=sec(x),y=1,x=−1,x=1 Step 1:…

Q: Evaluate the triple integral xyz² dv, where B is the rectangular box B = = {(x, y, z) | 0 ≤ x ≤ 1, −…

A: I=∭Bxyz2dV,B={(x,y,z)∣0≤x≤1,−1≤y≤3,0≤z≤2},

Q: Determine whether the series converges or diverges. Σ k = 1 converges diverges - (4k − 1)(k² – 1) -…

A: The given series is

Q: Use g(x) = 1½ (x + 5)² - 1½½ to answer the following. Remember to give exact answers. (a) Solve g(x)…

A:

Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

A: (a) To find the derivative function  for the following function f.(b) To determine an equation of…

Q: point P(-7,0,7) and parallel to the line x=4t+7, y=2t-6, z=3t-6

A:

Q: (BC Topic) (Technology Permitted) A polar curve is given by the tangent line to the curve at Select…

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Q: Given vectors = (5,-3) and = (-3, -6); find 4ū O=(12,32) ού = (8, 36) οὐ = (-32, -12) 0 = (32, 12) ο…

A: The objective of this question is to find the result of the scalar multiplication of the vector u by…

Q: d²y (BC Topic) What is dx² if x=5+21³ and y=4-31²? Select one: a. O b. 61 614 Oc. 614 1 O d. 22

A: dy2d2y​=6t41​ Option B is correct. Explanation:

Q: It has been determined that the number of fish f(t) that can be caught in t minutes in a certain…

A: Option A is correct.  f(39)=10 which means that approximately 10 fish can be caught in this pond…

Q: 6

A: Area = 7.0759Explanation:NOTE: We will use radians in this problem. The hint mentions the two parts…

Q: The normal to the curve: y = 12 has a gradient of -0.2 when x = 2. What is the value of a? - a x 88

A: Need to find out the value of a.

Q: 16

A: Volume= 128/3Explanation:

Q: Sketch the region of integration determined by the limits of integration and then switch the order…

A: for region graph is given below changing the order dxdy to dydxnew limits are…

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: 8x4−15x2+cExplanation: