Use Laplace transforms to solve the following initial value problem S y( (t) – y(t) = 8 (t) y(0-) = 1Ay'(0-) ="(0-) = y" (0-) = 0 %3D %3D

Q: Evaluate the following definite integral.  4

A: topic- definite integral

Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

A:

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)3 Σ 00 f(x) n =…

A:

Q: 8. Describe the steps you would use to determine the absolute extrema of the function Ax) = (x- 3)e"…

A:

Q: Use series to evaluate the limit. 4 3 sin(2x) – 2x + lim 4/3

A: Given problem:-

Q: 0 in quadrant II, find the exact value of: 81 If sin 0= sin 0+ sin 0+ 6. (Type an exact answer using…

A: topic - trigonometric identities sin(a+b)=sin(a)cos(b)-cos(a)sin(b)

Q: Evaluate the limit using L'Hospital's rule 14* – 3" lim

A:

Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: If f) = x*/x³ ++2 then 13x + 20x 2Vx +2

A:

Q: Write the first five terms of the sequence {an}. 1 (-1)n + 11) a1 = 3, an + 1 = an

A: We can solve as follows

Q: Using (sin x) = cos x and (cos x) = – sin r dr dr Show that # (cot x) = - csc² x dr

A: We need to show that ddx(cot x) = -csc2 x Given ddx(sin x) = cos x and ddx(cos x) = -sin x

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: we are given the function f(x)=cos(x) and the interval -π3,π3.The function f(x) is continous on the…

Q: Which of the following is a parameterization of the line that passes through the point (1, –3) with…

A: First frame the equation then verify all the given option.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your cnswer to two decimal piaces when…

A: Solving

Q: -2- At the point shown on the function above, which of the following is true? O f' > 0, ƒ'' > 0 Of'…

A: If the second derivative is positive then the graph of the function is concave up.

Q: Find the derivative with respect to x. (c) y = v7x – x4 (d) y = (1+ sin 7.x)-5 (a) y = (5x – 2)*…

A: This question is related to derivative, we will solve it using given information.

Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt' the product directly…

A:

Q: integral

A: We will solve the definite integral.

Q: 1 dx X +x13

A:

Q: Find the first derivative with respect to the domain variable for the following functions. 4. f(x) =…

A:

Q: 24) Identifa tue internel of convergen ce of a power ser's Ž (3)" n-1 (-3)", n=) a ) b) c) d) 3 2x23…

A:

Q: (2, 4) y = 2x ng a vertical element of area, he area of the shased region is gven by the integral

A:

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: dy (1- y)

A:

Q: petdo eidj to noitom paidi b noit t no eog edt bnt Use the limit process to find the area of the…

A:

Q: %3D Find the area of the region bounded by y = 5x² + 1, x = 0, x = 2,y = (

A:

Q: Find the limit: 4z4 – 4y4 lim (1,9) → (3,3) 4yª z² - y?

A: lim(x, y)→(3, 3) 4x4-4y4x2-y2

Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: Find the area of the shaded region. ¡y = x² + 1 ... 5 y = x 2 A B D

A: Area of a bounded region by curves is given by ∬dydx.

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: rrent Attempt in Progress Find r'(t). r(t) = (tan-'(9t))i+t cos(t)j – v NOTE: Enter your answer in…

A: We have to find the derivative

Q: 15. Find x² (2x³ + 4)5 dx

A:

Q: (4, 4) y= 2x-4 (1,-2) Jsing a horizontal element of area, the area of the shaded region is given by…

A: As required, draw a horizontal stripe as shown:

Q: Use the definition of Taylor series to find the first three nonzero terms of the Taylor series…

A:

Q: s @ = 135° a solution to the equation sine = cos 0. Justify your answer and explain the approach you…

A: Given query is to find that statement is true or not.

Q: Find the sum of the series. s 7(-1)"72n + 2n + 1(2n + 1)! 00 Σ n = 0

A:

Q: Find the value of the series: 1+2" 3n-1

A: We have to find sum of series.

Q: dy for x'e*y Find dx sin' ( 3x) + In (y) by using implicit differentiation.

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

Q: Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x² – 3x + 8…

A: Here We have to use the definition of the derivative.

Q: long

A: We will use long division method.

Q: Solve  x * (dy/dx) – x6ex = 4y

A: on solving this we will get :-

Q: y = xx, x-4, and y =0 Revolve the area of the shaded region about the line x- 4. Using circular disk…

A:

Q: Evaluating Indefinite Integrals - Partial Fraction Decomposition Suppose we want to evaluate the…

A:

Q: 12. The demand function for 66 piece Tinkertoy set is D(q) 750 and the supply q+1 function for…

A:

Q: Find the limit. 421 (a) lim 7+ 17 (b) lim x-0 X 3

A: Topic = Limits

Q: Step 3 Apply the Fundamental Theorem of Calculus, which states that f(x) dx = F(b) - Fa). Use this…

A: We can complete step 4 by the cross multiplication method.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: If f(x) = (x2 + 5x + 8)*, then f'(x) = f'(5) =

A:

Q: estion 6 of 10 w Policies rent Attempt in Progress Find V (V × F) if F(x, y, z) = 8 sin xi + 3…

A: We know divergence of curl of any vector function is zero.