A Find the area bounded by the curves, the axis and the given values of x. Sketch the graph. 1. y=4-x and the x - axis.

Q: Find the Maclaurin series for the given function f(x) = e-6x

A: The maclaurin series is: f(x)=e-6x     ,    f(0)=1f'(x)=-6e-6x     ,    f'(0)=-6(1)=-6f''(x)=36e-6x…

Q: Find V x (V × F) if F(x,y, z) = 8xyj+ 4xyz k. V × (V × F) = (4(y+2), 4:x, 0)

A:

Q: 6. What is the general solution of the following differential a²y.cdy d²y equation -52…

A: We need to find general solution.

Q: 2. y = e*cos (2x) is a solution to y'-bytoy=0 3X

A: 2.y=e3xcos2x is a solution to y''-6y'+13y=0

Q: xー1 dx (x+1) (x-3)5

A: Use substitution method for solving the  integral.

Q: Let T10 (x): be the Taylor polynomial of degree 10 of the function f(x) = In(1+ x) at a = 0. Suppose…

A: The possible value of x for which this approximation is within 0.001 of the right answer is 0 < x…

Q: у? — 4у — 21 Зу2 — 17у — 28 imy→7

A: Given query is to find the limit of the expression.

Q: ニ。

A: Given query is to find the solution of the differential equation.

Q: Solve using quotient rule:  f(x) = (3x^2 – x + 4) (2x^2 – 1)

A:

Q: Evaluate the definite integral. e16t i + e¬tj +t k )dt O el6 – 1 (e-- - 1) + i+ (e-1 – 1) j + , k 16…

A: To solve the given integral.

Q: What is the domain of y =f"(x) if f(x)=;(x-1)*?

A:

Q: for the N(0) is it 0k? or can I write it just k?

A: Yes, N0=-12i+12j+0k.

Q: valuate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A:

Q: 2 X+2| dx -3

A:

Q: Determine the largest interval that pλ must lie in to approximate p with a relative error of at most…

A: 3. Determine the largest interval that pλ must lie in to approximate p with a relative error of at…

Q: Find the volume of the solid Formed by revolving the region bounded by the graphs OF y=x +1, y = 0,…

A: Find your answer below

Q: Determine if the following function is continuous or discontinuous at x = 0? 4z +5 f(2) = %3D 9- 32

A:

Q: Prove the statement by mathematical induction. 3+5+7+…+(2n+1)=n(n+2) 1. Proposition is true…

A: The given statement,   3+5+7+....+2n+1=nn+2

Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

A:

Q: Q1: Find dy/dx for the following functions:- (1) e – 3* = x sinh y (2) tan-12 = (Inx' + y²)

A:

Q: 3/2 <(のーメ)CK dx 2. 2.

A:

Q: 7. Į V1- xdx 8. ſ e2x dx

A:

Q: If y = In dy then dx 10 10 20 et - E) eT – 10 A) x – B) eT D) 0 eT – 10 10 — еT Of –

A:

Q: 2. A rocket is launched in the air. Its height (in meters above sea level) as a function of time t…

A:

Q: Find the domain of r(t) and the value of r(te). NOTE: Reund your anser to two decimal places uhen…

A:

Q: Obtain the inverse transform of the following 2s-3 1. s2-9 10 (3s2+12) + (s²–25) 3s-2 3.…

A: As you have asked multiple questions so I have answered only first question as per the…

Q: 3- the solution for the following O.D.E y' = In(x) + tan (x) %3D

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: sin(x) dx B. Evaluate the integral 1- sin? (x)

A: Our Aim is to evaluate the integral ∫sin (x)1-sin2 (x) dx

Q: Find the area of the region bounded by the curve y = 9- x2 and the x-axis. Answer:

A:

Q: Find the value of each of the six trigonometric functions of the angle 0 in the figure. a = 5 and b…

A:

Q: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) cor…

A:

Q: 5sin e Cose de Sin? o +3 Sine -4 2.

A: Solve the following

Q: Find two positive numbers that satisfy the glven requirements. The second number Is the redlprocal…

A:

Q: Find the area bounded by y = x + 4 and y = x² - 2. Answer:

A:

Q: Find the height of the tower using the information given in the illustration. 84.239° 120 ft The…

A: topic - trigonometric ratios tanθ=oppositeadjacent

Q: 1. Rules of LDef nite Integrals: 12 a) b) rpx 12 12 f(x)dr 4, find the If f(z)dr = 12, " $(z)dz = 6…

A:

Q: Given t2 – 4 f(x) = dt 1+ cos2(t) At what value of x does the local max of f(x) occur?

A:

Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i + 11 sin(t)j +…

A: Let's find.

Q: Find both first partial derivatives. z = 10y² Vx Oz dz %3D %3D

A:

Q: There are some instances when an abbreviated form of the distance formula can be used. What is the…

A: Please see the below picture for detailed solution.

Q: To evaluate the Integrals, use the additive Interval property of Integrals which Is glven as…

A: answer is in next step

Q: Evaluate the definite Integral by the limit definition. Step 1 To find the definite Integral dx by…

A:

Q: x +1 Evaluate the given limit of lim if it exists. 2→-1 x4 – 1 O limit does not exist 4 O -1

A: We have to find the limit

Q: 5. Í sin 2e de 6. ſer cosh x dx

A: We have to integrate and have to check the answer

Q: Question 3 Suppose C=0, so that 2y 24y 5x3 = 0. Find all points (x,y) at which the tangent line to…

A:

Q: t*dt then If f(x) = 3 f'(x) =

A:

Q: 9. S (6eº+1)/½ eo 10. |(1 + 2x)³ dx

A: We can solve as follows

Q: mental Theorem of Calculus to fin

A:

Q: What is an equation for the cosine graph shown below? 11 -10 -8/ -6 -5 .4 -3 -2 -1 -135 -90 -45 45…

A: