e3x Let dx be given . If u = e* + 1, then the resulting integral is S f(u) du. Compute f(3). ex+1

Q: Answer the questions for the function f(x) = - 3x + 3x2 - x a. Find formulas for f' (x) and f'(x). f...

A:

Q: Given: (25(x)dx e-x3 There is a function f (x) such that when u = -x³, the resulting integral is Eva...

A: topic - functions

Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

Q: Use the Laplace transform to solve the initial value problem below: b) y" + 3y' + 2 y = f (t) Where ...

A:

Q: A statue 3 m high is standing on a base of 4 m high. If an observer's eye is 1.5 m above the ground,...

A: Solution is written in below steps.

Q: Q9

A:

Q: Obtain the general and particular solution 1. 2ydx = 3xdy, when x= 2, y = 1.

A:

Q: Consider the following system on (-1,∞0) × (–1, 0), 2y 2x 1+ Y 1+x 1. Find all the equilibrium point...

A:

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

A:

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 k + 7 k(k +...

A:

Q: Use the formula for the binomial series: m(m-1)..(m-k+1), (1 + x)" = 1+ mx + m(m-1)2 2! ... m(m-1).....

A:

Q: Find the derivative of the function. f(t) = 8r2/3 - 4t/3 + 8 f '(t)=

A:

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

A:

Q: Evaluate the integral. x2 e dx +C

A: Here, to evaluate: ∫8 x2exdx=8∫x2exdx

Q: Eliminate the parameter to find a Cartesian equation of the curve. x(t) = t² + 5 y(t) = 40 – 8t (a) ...

A: We have to solve the given question

Q: Using u-substitution, the integral f(x)dx reduces to a new integral f g(u)du. If g(u) : u+1 evaluate...

A: ∫f(x)dx = x + ln(x-1) +c we have to find f(x) so we have to derivate the ∫f(x)dx so f(x) = 1 + 1/(x-...

Q: Current Attempt in Progress Use the ratio test to determine whether the series converges or diverges...

A:

Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x) 

Q: Solutions of differential equations: y' = sin x O y = - cos x +c O y = cos x + c %3D

A:

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent (-1)*+1 5k

A:

Q: Use the formula for the binomial series: (1 + x)" = т(т-1) 2 2! m(m–1).-(m-k+I),k + + 1+ mx + %3D .....

A: The maclaurin series for 1+x7

Q: 48. h'(x) if h(x) 2+9

A: Here, the given function is: h(x)=e2xx2+9 To find the first derivative of h(x), using the quotient r...

Q: Please answer the last 3

A:

Q: an exponential function y f(x). (2,8.64) (1,7.2)

A:

Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: Obtain the general and particular solution 3. xcos²ydx + tanydy = 0

A:

Q: Using the partial fractions technique, the function f(x) = 37x+82 can be written as a sum of partial...

A: ∫37x+82x2+2x-24 dxConsider 37x+82x2+2x-2437x+82x2+2x-24=37x+82(x-4)(x+6)37x+82(x-4)(x+6)=Ax-4+Bx+637...

Q: If f(16x*- 16x³ + 4x²)dx = F(x) + C, then F(x) %3D

A: Formula:∫ xn  dx  = xn+1n+1 + C   Integral:I=∫ (16x4-16x3+4x2) dxI=∫ 16x4 dx -∫16x3 dx +∫ 4x2 dxI=16...

Q: 2e 7. Evaluate ds

A:

Q: Find the exact value of the expression. cos(tan-1() 35

A:

Q: Evaluate the limit below. 1 lim (x,y)→(0,0) 1-x2-y?

A: limx, y→0, 011-x2-y2

Q: k If u = f(x), then f dx x4+2x²+1 +C for some constant k . Compute kf(1). x2+1

A: topic - functions and indefinite integral

Q: Use sigma notation to write the Taylor series about x = xo for the function. 4 In x; xo = 1

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…=0+ddx...

Q: Evaluate the integral. 15e cos(2x) dx +C NOTE: Enter the exact answer.

A: This question is based on indefinite integral.

Q: S 4x -Ry +32 = -2 2x +2y + Sz = 15 X+2y+3z=-3 -1x ty-2= 6 ! 3x-3y +22 = -4 ち=えも-s-x8 14+3x+2< 4y-2x ...

A:

Q: 2:(y –x² }tx+ dy =0 1.

A:

Q: Find the volume under the paraboloid  z = 4x2 + 4y2,  above the xy-plane, and inside the cylinder  ...

A:

Q: Determine whether the series converges, and if so find its sum. 4k+2 Σ 7k-1 k=1 1) This series can b...

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve, for - くtく æ(t) = 4 tan? t y(t) = ...

A: Given

Q: Evaluate the integral. 7 sin-x dx +C NOTE: Enter the exact answer in expanded form.

A:

Q: y = cje + c2er

A:

Q: Find a parametric representation for each of the following surfaces: (a) 36(x-1)² +25,y² +9(z+2)² = ...

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other...

Q: 1 (ke)3x For ſ k*e3*dx = + C. If u = 3x, then k =? 3 (1–In 2-1)

A:

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A: As we know that the nth order Taylor's polynomials at x=x0 is given by; pn=fx0+x-x011!f'x0+x-x022!f'...

Q: Suppose that f(z) is an entire function and there exists aceR s.t. Re(f(2)) < c for all z. Show that...

A:

Q: Given A=-3ay +2ax +4az, B=3az -2ay + 5ax and C=-3ax +4az +5ay. Find a. A+2B-C and b. I 2A-3B+C I.

A: Given A=2ax-3ay+4azB=5ax-2ay+3azC=-3ax+5ay+4azA+2B-C=2ax-3ay+4az+10ax-4ay+6az--3ax+5ay+4az          ...

Q: FIII in the yellow box to complete the truth table of "p v (q →r) V q->r "p v (q →r) r 5.

A: Concepts:   ~ p is oppostite of p.p=T then, ~p =Fp=F then, ~p =T   Implication Truth table:   Disju...

Q: dx O arcsin(x' ) + C O arctan(x*) + C 8 O arcsin(x³ ) + C O arctan(x') + C O arcsin(x ) + C

A:

Q: Find the unit vector of A=3ax+2ay-3az

A:

Q: B In Problems 31-40, find the intervals on which the graph off is concave upward, the intervals on w...

A: Find your answer below