Find each limit, if it exists. +1 (a) lim x→∞0 x4 5 (b) lim x00x³ +1 5 (c) x³ + 1 lim x→∞0 x2 - 5

Q: Find the area of the region bound above by y = 2cosx and below by y = secx,-π/4 ≤ x ≤ 1/4.

A:

Q: The base of a three-dimensional figure is bound by the line y = -x + 1 on the interval [-3, 0].…

A: Solve the following

Q: The f2e4t sec2e4t dt is {A} = = tan e 4t + C {B} = sec³e4t + C 16 {C} /e4t tan e4t + C {D} et…

A:

Q: Question 10 Given: y = xcos (x); Find y'". O(E) None of these Oy" xsin (x) + 2 cos(x) Oy" asin (x) -…

A:

Q: Test the series for convergence or divergence. n+5 Σ n=1 n³-1 Show all work using the limit…

A:

Q: Find curl(F x G) = V x (F x G). F(x, y, z) = i +5xj + 3yk G(x, y, z) = xi - yj + zk

A:

Q: For the following: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the…

A:

Q: Evaluate: sec²(4t) [3-tan(4t)]³ dt a.-16 [3-tan(4t)] + C b. | [3 –tan(4t)] + C 4 OC. 1 [3-tan(4t)]…

A: integration

Q: Evaluate. (Be sure to check by differentiating!) 6 7 STOCK *XX=-=-= dx, x# 7 + 6x 6 6

A:

Q: Evaluate fi fi fi (xy+z)dxdydz Note: input your answer in two decimal places (example: 1.05, 2.53,…

A:

Q: 32 Question * (3 Points) The proper transformation for sin²x to make the f sin²x dx readily…

A: substitution

Q: 9. (y³+4)√1- cos² (y4 + 16y) ». f (y ³. cos(y¹+ 16y) () 2. dy

A: Answer of the above integration is

Q: 3. y = (x+b)(x-a). (x-b) ; y

A: A detailed solution is given below. Use logarithmic differential to solve it.

Q: 1. An undamped spring-mass system with mass m = 2 and a spring constant k = 8 is suddenly set in…

A: Solution in step 2

Q: Find the laplace transform of f(t) = 2t¹-3e³t+10 cos 2t

A: Given that,  f(t)=2t4-3e3t+10 cos2t

Q: An equation of a conic is 5 r = 3+2 sin 0 Identify the conic, find the eccentricity, write an…

A: A conic section with a focus at the origin, eccentricity e, and directrix at x=±p has polar…

Q: h(x) = f(gx)) calculate the following derivatives using the table a) h'(3) b) h'(2)

A: Given

Q: Determine whether the improper integral diverges or converges. 00 √x³²e-x dx O diverges Evaluate the…

A: To find the integral: ∫0∞x2e-xdx converges or diverges.

Q: Evaluate the iterated integral. 16-y² ST Jo (x + y) dx dy

A:

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

A:

Q: 37-38 Evaluate the integrals by completing the square and ap- plying appropriate formulas from…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find the laplace transform of ƒ (t) = 6t³ + 4t² – 3 OF (s) -3s³ +8s+36 84 OF (s) 36s³ +88-3 84 OF…

A: A detailed solution is given below.

Q: The base of a three-dimensional figure is bound by the line y = √x + 2 on the interval [-1, 1].…

A: We have to find the volume of bounded region in the interval [-1,1].

Q: Current Attempt in Progress Find the exact arc length of the curve .x = 1 = = √ ( ₁² + 2) ²/² ₁ +…

A:

Q: 2. Evaluate each of the following limits using the function f(x), defined below. If the limit does…

A: The given function is: f(x)=x+3x2+5x+6

Q: Find the limit. NOTE: Enter the answer using round brackets. 1 lim (12²2 +9.7) = (17.00) 9't

A: Given : A value that a function approaches the output for the given input values Here, it has been…

Q: 1. Given the following matrices: A = 1 2 3 4] 24 6 8 1 3 5 7 -1 2 -3 4 a. [(AC)BT] - DT b. [(BD)…

A:

Q: Show that the Differential Equation is EXACT and then solve it. 2. (cos2y - 3x2y2)dx + (cos2y-…

A:

Q: Find the laplace transform of f(t) = 21² +41 - 5 F (s) = F(s) = O O -5s² + 4s + 4 53 -555 +454 45³ -…

A:

Q: Determine whether the improper integral diverges or converges. 6° x²ex dx converges O diverges…

A:

Q: Evaluate the following 2- S ( 37/3 + 5x² + 3) dx

A:

Q: x²-3x - 7 √(x² + x + 2) (2x - 1) dx

A:

Q: y Given: xe² + In(x - y) = . Find dy/dx. dy 2x(x-y)-x¹+x -w) (20

A:

Q: 2. (4x³-3)dx

A: Let's find.

Q: أ 12, x > 1 (b) ) 5 f(x) dx

A:

Q: 10. | x³(lnx+1)8x* dx

A: To evaluate the integral: I=∫xx(ln x+1)8xxdx=∫8xxxx(ln x+1)dx

Q: a) Graph the function f(x)=x² + 2x b) Draw the tangent lines to the graph at the points whose…

A:

Q: b) Determine whether the series n=1 find its sum. Show All Your Work! n-l is convergent or…

A:

Q: Write the conjugate of √a +3

A:

Q: 1 (s² + a²) (s² + b²) a sin at + b sin bt a² - b² b sin at a sin br - ab (b²-a²) cos at + cos bt…

A: This question can be solved using the concept of inverse Laplace transform.

Q: (a) f(x) = 2x³ + 3x² - 12

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question..…

Q: Find the equation of the line tangent to the graph of f(x) = (In x)² at x = 7. MER y= (Type your…

A: Find the derivative at the given point and write the equation of tangent line using slope point…

Q: 3. For the double integral [['sin(y) dydz I (a) Sketch the region of integration. (b) Change the…

A: Given; I=∫01∫x1siny2dydx   As we know that; ∫sinxdx=-cosx+C

Q: A 10-foot ladder leans against the side of a building. If the top of the ladder begins to slide down…

A:

Q: The table shows a proportional relationship between the number of tickets purchase and the cost.…

A:

Q: approximate with accuracy 10^3 to the solution of x³+x-4 = 0, lying in the interval [1,4].

A:

Q: Find the value(s) of k such that the function x≤ 2 (x³ + k x³-8 f(x) = x > 2 ) x-2 is continuous at…

A:

Q: If f(x) = sinx and g(x) = cosx, then what is the relation between g'(x) and f""(x)?

A:

Q: Use the method of Laplace transforms to solve (O) 0 (0) 0.

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: Find your answer below