1. Find the area of the region bounded by the given curves. Show the computed areas of sections using a graphing tool (Desmos, Geogebra or Autograph). It should be parallel or equal to the manually calculated areas. Strictly use definite integral in solving for the area. a. y = Vx and y = x3

Q: A ball is thrown into the air and its position is given by h(t) = - 4.3t2 + 41t + 15 where h is the…

A:

Q: Calculate the following derivative if f(x) = 5e* - x³. %3D (Use symbolic notation and fractions…

A:

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

A:

Q: Step 1 |an + 1 an + 1 n+ 1 1, or lim = 00, then n00 an Sa, diverges. For any fixed value of x such…

A:

Q: 850 b. 450

A:

Q: 4) Find all values in the interval [-2z,27]at which the graph of fhas a horizontal tangent line.…

A: -2pi = -6.2832 2pi = 6.2832 we can see from the graph 5 values satisfies horizontal tangent, we can…

Q: Expand the binomial using the binomial theorem. Show all of your work. (z- 4) °

A:

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

A:

Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

A:

Q: Fit a second degree parabola y = ax² + bx + c to the following data %3D 3. y 1.8 1.3 2.5 6.3

A: Normal equations associated with y=ax2+bx+c are: ∑y = a∑x2+b∑x+nc ∑xy=a∑x3+b∑x2+c∑x…

Q: Find the following using the table below. 1 2 3 4 2 4 1 1 4 9(x) 2 4 1 1 4 2 (a), 6 h'(4) if h(x) =…

A:

Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

A:

Q: Step Solve for c. Use inverse trigonometric functions to find the value of c guaranteed by the Mean…

A:

Q: fF(x)dx = -9 and Si (x)dx = . 3 tind f(x)dx Given that

A: We can solve the answer using the properties of definite integral as below.

Q: 4) Find all values in the interval [-27,27]at which the graph of f has a horizontal tangent line.…

A: topic- functions and derivatives

Q: State where the power series is centered. (-1)"(2n – 1) „n Σ * 2"n! n = 1

A: Solving

Q: Indicate a general rule for the nth term of the sequence when a, = 2 and r =. 3. a, = (2)(J)*| n+1…

A:

Q: If we apply Rolle's Theorem to the function f(x) = 2x? – 4x – 7 on the interval [ – 1, 3], how many…

A:

Q: Find an explicit formula for an. 15) 0, -1, 0, 1, 0, -1, 0, 1, . . .

A:

Q: Determina the vector field of F. F(1, y) = yi -j

A: Please see the below picture for solution.

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

A: We have to apply circular discover method to solve the problem

Q: A farmer finds that if she plants 90 trees per acre, each tree will yield 30 bushels of fruit. She…

A:

Q: The junior class has 50 students. Fifteen students take only French, 5 students take only Latin, and…

A:

Q: Let f(x) = - 5 sec(6x) f (x) =

A:

Q: integral

A: We will solve the definite integral.

Q: The probability that an event will happen is . What is the probability that the event will not…

A:

Q: The ODE below models a spring, mass, dashpot system with damping constant c, spring constant k and…

A:

Q: . Tind the general solution of the given variable separable can ation. O 20oSx dx - 3sinx Siny dy =0…

A:

Q: Find the coordinates at times t = 0, 5, 10 of a particle following the path a = 9+ 5t, y = 2 – 7t3.…

A:

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: 16 Indicate the general rule for the arithmetic sequence with a3 = 8 and a8 = 33. a n = 2 + (n -…

A: The nth term of an arithmetic sequence is an = a + (n - 1)d  a is the first term. d is the common…

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 5 sec2 x dx -T/6

A:

Q: Given f"(x) = 7x – 3 and f'(-2) = -6 and f(-2) = 6. Find f(4) %3D |

A: Here we will find f(4),

Q: short

A: Please refer to the image below

Q: 4- to --6 -5 -4 -3 -2 -1 5- ver which interval of z values is f'> 0? о (2, о) O 12, 0) 0(- 00, 2)…

A:

Q: 9. Find the local and absolute extreme values on k(x)=(x-2)° +3 on | the interval [0,5].

A:

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

A: Given problem:-

Q: Evaluate the following limits. If needed, enter oo for oo and -oo for – 0. V5 + 6x2 (a) lim 3+ 10x…

A: Use the substitution and then simplify the limit.

Q: pind tue indefinete integral S In(s-1) ds

A: ∫ slns-1dsLet u=s-1=∫u+1lnudu=lnuu22+u-∫12u+2du=lnuu22+u-u24+uSubstitute back…

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

A:

Q: -2

A:

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

A:

Q: Find y ify=xIn(9x+1) 2.

A:

Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: Evaluate the limit 5+ 9x lim 1+00 3 – 4x

A: Given problem:-

Q: (-1) ntl n=1 n3

A:

Q: Solve the system of differential equations.

A:

Q: Find r'(t). r(t) = (tan-(4t))i+t cos(t)j – Vtk NOTE: Enter your answer in terms of i, j, and k.…

A:

Q: Setup the iterated integral using the order dydx and dxdy. Sketch R. // (Va+ e") dA where R= {(x, y)…

A:

Q: Find an interval of t-values such that c(t) = (cos t, sint) traces the lower half of the unit circle…

A: Given that ,  c(t) =cost, sint,  we have to find an interval of t-values such that it traces the…