).  Find the Taylor series at a =  ? 2 for f(x) = 4 cos(x). ∞       n = 0   please hsow step by step clearly .

Q: 3.The height, in metres, of an object that has fallen from a height of 180 m is given by the…

A: We have to find the velocity and average velocity.

Q: Determine whether the series is convergent or divergent. co n = 2 O convergent Odivergent 9 n In(n)

A: To determine whether the series is convergent or divergent. ∑n=2∞ 9n lnn

Q: 2. Solve the equation for x. Pay attention to the domain of the natural log: In In x + ln (2x + 1) =…

A:

Q: Find the length of the curve: a) y=x^(3/2) +8 on the interval[0,2] b) x=(y^5)/5+1/(12y^3) on the…

A:

Q: Find the critical points of the following function. 19 f(x) = 4x³2x²+ x2 + 5x Select the correct…

A:

Q: how many triangles b = 19 mine <A = 26° a = 14 T 1 form if :

A:

Q: Evaluate the surface integral. x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies above…

A:

Q: Find an antiderivative of 7 z4–9 z6 27 Antiderivative = in the variable where x > 0. Remember to…

A:

Q: Area = [-1, "]: Consider the following solution to the problem of finding the total area bounded by…

A: Consider the following solution to the problem of finding the total area bounded by the graph of…

Q: Determine whether the series converges or diverges. 8 n=1 converges Odiverges 1 + sin(n) en

A: We need to determine convergence.

Q: e area under the given curve over the indicated interval. 8) y = 7; [2, 9] 8- 7- S 4+ 3+ 2+ 1 A) 14…

A: Given query is to find the area of the curve.

Q: -10 -8 -6 -4 * * * 8 -10 Y 2 4 6 8 f 10 x

A: Option 1 Given parametric equation is x=t, y=2t Now y=2t⇒y=2x Graph of y=2x is as

Q: | 1 3 2 1 1 To find the blue shaded area above, we would calculate b få f(x) dx Where: a = f(x) = 2…

A:

Q: Differentiate implicitly to find d2y/dx2.   x3-y3=12

A:

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 7 sin(t). The initial…

A:

Q: Find the function's absolute maximum and minimum values and say where they are assumed. f(x)=x 5 3…

A:

Q: A 7ft ladder leans against the side of a house. How far is the bottom of the ladder form the side of…

A:

Q: consider the following function: F(s) = s²-s+1 s³+6s²+11s +6 652 3

A: L-11s-a =eat

Q: Solve the following equations x + y = 4 3x – 4y = 5

A:

Q: Locate the critical points of the following function. Then use the Second Derivative Test to…

A:

Q: 25. Show whether the following function is continuous et x = 0. 4x-9if x>-3 3x+6 if xs-3 f(x)=

A:

Q: +-1²-)-(4-44)dy

A: ∫yndy=yn+1n+1+c

Q: A ladder leans against the side of a house. The angle of elevation of the laser is 63 degrees when…

A: Let x be the distance of top of ladder from the ground.

Q: b)y= 4 x-2 ,(6,1) c)f(x)=√√x+4,x=5

A:

Q: Looking up Kevin sees two hot air balloons in the sky. He determines that the lower hot air balloon…

A:

Q: Find the Maclaurin series for f(x) = cos(19x). cos(19x) = Σ n0

A: As we know that: Maclaurin series for the cosx centered at x=0 is given by f(x)=∑k=0∞(-1)kx2k(2k)!…

Q: Evaluate: ²dz dy dx Ꮭ x 4+4 O π/48 O tan-¹(2)/24 O π/96 π/24 OT

A: The given integral is: ∫02∫0x3∫0y zx4+4 dz dy dx

Q: 2- Calculate M6 for f(x) = √10x on interval [0, 2].

A: Given:     fx=10x on interval 0,2 The M6 (also known as the midpoint approximation) uses the…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400…

A: A microwaveable cup of soup package needs to be constructed in the shape of a cylinder to hold 400…

Q: 4. Use the method of substitution to find evaluate the following indefinite integrals: sin(x) cos³…

A: We need to solve integrals.

Q: 5. y = 3sin (2x²)

A: Solution: Given data, y=3sin(2x^2)  dy/dx = d/dx [3sin(2x^2)]

Q: 2). Find the Taylor polynomial of degree two approximating the given function centered at the given…

A: According to question,Given Function,fx = cos2x

Q: Determine whether the series converges or diverges. Σ(1+1) (¹ ²0 n = converges diverges e-n

A: We can check whether the given series is convergent and divergent .

Q: Find the area between f(x) = x² - 16 and the x-axis from x = 0 to x = 8.

A:

Q: Perform a first derivative test on the function f(x) = 2x³ + 6x² - 48x+6; [-4,6]. a. Locate the…

A: From given function we have to find the value of vritical points. We also find local minima and…

Q: 14) f 118 dx X A) 118x + C B) 59x-2 + C C) In 118 + C D) 118 In x + C

A: See this solution in below.

Q: Speedometer readings for a vehicle (in motion) at 14-second intervals are given in the table. t…

A: we need to find the distance travelled

Q: Find an equation of the line passing through the (1, 2) and the point intersection to the lines 3x +…

A: The line passing through the (1, 2) and the point intersection to the lines 3x + y =5 and 2x - 5y -…

Q: ďy dx² If xy + 2 = -x then find y at the point (1, -3) in simplest form.

A:

Q: y = x², y = x

A: Here is the solution:

Q: 26. Use the limit definition to compute f(x) if f(x) =12x²+2.

A:

Q: Find the length of the polar curve r = 8 sin³ (0/3) on 0≤0 ≤π/4.

A: The arc length of a polar curve r=fθ between θ=a and θ=b is given by  ∫abr2+drdθ2dθ Given: r=8sin3θ3…

Q: 16. A function s(t) represents the position of an object based on time t in seconds. Determine what…

A: Solution: Given data, Position of an object = s(t)

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 2t, y = 4t,…

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A:

Q: 211. Revisit the 1-foot radius circular saw blade with the one red tooth. Look at the ratio m of the…

A:

Q: Express the number as a ratio of integers. 1.580 = 1.580580580...

A: Given: Number is 1.580580580.....

Q: For the demand function q=D(x)=700/x​, find the following. ​a) The elasticity ​b) The elasticity…

A: Given, The demand function q=D(x)=700/x​,

Q: 6. The Statuary Hall in the Capitol Building in Washington, D.C. is a whispering chamber. Its…

A:

Q: Find the average value of the function f(x)=x²-7 on [0,6]. The average value of the function…

A: Given f( x ) = x2 - 7 given interval = [ 0 , 6 ] Average value = ∫abf( x )dx