2. Use first principles to find the derivative of each. f(x) = √√2x − 1 a) b) y = x₁

Q: 1 - Use the graph of ƒ (x) = below to find a number & such that |ƒ (x) — 0.5| < 0.2 whenever 0 < x −…

A:

Q: Determine if the series converges or diverges. If the series converges, find its sum,

A:

Q: f(x) = e-5x, a = 0 OA) 1-5x + 2²-125³ 2 6 OB) 1-5x + 22²-15³ 2 3 OC) 1-5x + 2²-1¹ 25x2.125x3 18 OD)…

A: fx=e-5x Taylor polynomial  at x=a=0⇒fx=f00!x0+f'01!x1+f''02!x2+f'''03!x3+.....

Q: Evaluate Answer: ㅠ [²² P 4 sin Ꮎ dᎾ dr .

A:

Q: Consider the following definite integral. r3π/2 2 (t³ + sin(t)) dt Jπ/2 (a) Evaluate it "by hand,"…

A: ∫xndx=xn+1n+1+c ∫sinxdx= - cos x+c

Q: Let 7 be the plane given by 3x + y + 2z = 6. (a) Let be given by x = 2+1, y = 3t, z = t. Does…

A:

Q: 29. p = 200 - x 2x

A: Given question  29. p = 200 - x2x

Q: Given the function graphed below, evaluate the definite integrals. ¨¨` 3 2 1 -1 -2 -3 √ ² = Lª…

A:

Q: A car is moving along a straight road. At time t seconds, the position of the car (in feet) is s(t)…

A:

Q: ㅠ Si F. ¹ · dỡ where F = (3z, 0, −2x), and C' is given by r(t) = (t, sin(t), cos(t)), 0 ≤ t ≤ ñ…

A:

Q: Use the Limit Comparison Test for 4n² +9 n(n − 6)(n-14) ∞ Σ n=24 bn = an = an lim n→∞o bn M8 to…

A: The given series is (4n2+9)/[n(n-6)(n-14) ], n from 24 to infinity.

Q: 3. What is the line tangent to the curve x2 + y2 = 25 thru (2, 1)? A. 2x + y = 25 B. x + 2y = 5…

A:

Q: In Exercises 23-26, use the revenue function to find the marginal revenue for selling x units. 24. R…

A:

Q: Q1. Use the following graph to find: a) Range: b) Axis of summitry

A:

Q: Suppose F(t) has the derivative f(t) shown below, and F(0) = 4. Find values for F(1) and F(9) 2 1 -1…

A:

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 5 cos(8), y…

A:

Q: The population in millions of arctic flounder (a type of fish) in the Atlantic Ocean is modele 8t+96…

A:

Q: Speedometer readings for a vehicle (in motion) at 12-second intervals are given in the table. 012 24…

A: According to question, Interval of readings = 12 s, t(sec) 0 12 24 36 48 60 72 v (fts) 0 5 19…

Q: In Exercises 23-30, find an equation of the tangent line to the graph of f at the indicated point.…

A:

Q: 19. C = 4500 + 1.47x

A: For a cost function C( x ) , marginal cost function is given as marginal cost function = ddxC( x )

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 7x + 19 between x =…

A:

Q: T³ (x4+3) ¹ This can be transformed into a basic integral by letting Consider the indefinite…

A:

Q: Q4. The half-life of mass of 500 mg: Plutonium-210 is 140 days. Suppose that a sample of this…

A: The half-life of Plutonium-210 is 140 days. Suppose that a sample of this substance  has a mass of…

Q: Find the equation of the tangent line to the curve at the given point. 6x - xy + y² = 12 at (2,2)…

A: We are required to find: The equation of the tangent line to the curve 6x-xy+y2=12 at (2,2).

Q: Complete the first line ONLY of the derivative using the product & chain rule for the function: р =…

A: px=4-3xx4+7x3

Q: Evaluate the definite integral. 1 e² + 8 6² o e² + 8z dz

A:

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

A:

Q: Find the area between the curves. x = -5, x = 1, y = 4x, y = x² - 5 The area between the curves is…

A:

Q: Write an equation for the function graphed below y TY 9

A: Vertical asymptotes at x=4 and x=-2 so in denominator we have function like  (x+2)(x-4)

Q: Let s(t)= ael-² be a function for the position in millimeters of a particle as a function of time in…

A: Let position function denoted by s( t ) velocity function denoted by v( t ) acceleration function…

Q: In Exercises 19-22, use the cost function to find the mar- ginal cost for producing x units. 19. C…

A:

Q: Calculate the area of the surface generated by rotating the parametric curve c(t) = (t², 3t) about…

A:

Q: Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = x² + xy +…

A:

Q: x²

A:

Q: 107 107 Suppose that a₁ = 9 and b₁ = -28. Compute the sum. i=1 i=1 107 Σ(1ai i-1 (1ai - 10bi)

A: we have given ∑i=1107ai=9   and ∑i=1107bi=-28

Q: 4 The volume of a cantaloupe is given by V= ²³. . The radius is growing at the rate of 0.7 cm/week,…

A:

Q: Given the information below, estimate the total distance traveled during these 6 seconds using a…

A: Sum= Σk=0∆xf(k)  =∆x(f(0)+f(1)+ f(2)+.....f(n-1))

Q: Q14 Find the equation of the tangent line to f(x) = 3lnx - 5x at x = 1.

A: We have to find the equation of tangent at the given point. First we will find the y-coordinate of…

Q: 3. Find the Taylor series centred around zero for the function f defined by 5x-1 = e f(x) =

A: fx=e5x-1a=0

Q: Find the general solution for the differential equation. dy = = 12xy dx The general solution of dy…

A: dy/dx =12xy Find general solution of dy/dx = 12xy y =?

Q: The expression 729g¹y³√729g¹y³ = kg"y³ where: T = 8 = and k =

A: Given:  729g4y33729g4y3=kgrys To Find: To determine the values of r, s, and k.

Q: Find the exact average value fave of f(x)=√16-r² between 0 and 4, then find an exact number c in…

A: Given that , fx=16-x2 , x∈0,4favg=?

Q: The marginal cost for printing a paperback book at a small publishing company is mc(p) = $0.011 per…

A:

Q: Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If…

A:

Q: $4.3 Curve Length in Parametric The arc length of the curve defined by the equations z(t) = 12…

A:

Q: 5 Use the linear equation y =(x- x - 32), where x is the degrees Fahrenheit and y is the degrees…

A:

Q: Given the function graphed below, evaluate the definite integrals. N A 3 2 1 -1 -2 -3 Sőt [₁² f(x)dx…

A: Here we have graph of f(x) ,need to find the integral. Since integral is given by area under the…

Q: Find the solution of the exponential equation 1000 (1.08) 50,000 in terms of logarithms, or correct…

A: The given equation is solved for the value of t.

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = 15 - x, y…

A: To find the volume of the solid obtained by rotating the region enclosed by the  graphs of y=15-x,…

Q: Find / (+62+3) de + C

A: