5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a. y = fogoh(x) b. y gofoh(x) c. y = gohof (x)

Q: Evaluate I= I=S 2+41 Iti NJ Z 2 dz

A: This question is related to definite integration, we will solve it using given information.

Q: Identify the surface y − 3 = x² +.

A: Solution: Given data, y - 3 = x2 + z2

Q: ind the solution of the given initial value problem. y(4) 10y" + 25y" = 0; y (1) = 8+e5, y'(1) = 6…

A:

Q: Find the solution of with y(0) = 8 and y'(0) = 7. y = y" + 3y + 2y = 72e²t

A: 1f(D) eat = 1f(a)eat .

Q: Find the exact length of the polar curve. r=0², 0≤0 ≤ 6π

A:

Q: Find the equation of the langents to the graph y-x3 3x2-15x-20 at the points of the graph where the…

A:

Q: If f(x) = (3x + 2)−ª, find ƒ'(x). Find f'(5).

A:

Q: Determine the particular solution. (xy)dy – (3x² + y²)dx = 0; Y(1) = 1 O 3ln(x) + 12 = 1²² 2x² O…

A: Let's solve differential equation.

Q: The area of the surface obtained by rotating the curve y = √√x + 1, for 0 ≤ x ≤ 2, about the x-axis,…

A: Given :

Q: Solve the following system of equations. 3x+4y = 4 6x+4y = 16

A:

Q: You are making a rectangular box with a square base. Its volume must be 8 ft^3 . Find the dimensions…

A: A rectangular box with a square base. Its volume must be 8 ft3

Q: Find the points on the graph of the function that are closest to the given point. F(x)=x², (0, 9)…

A: f(x)=x^2, (0,9)

Q: Find the derivative of f (y) 30% In(y) Enclose arguments of functions, numerators, and denominators…

A: To find the derivative of the given function.

Q: Evaluate the integral using the following values. 8 [³x x³ dx = 1,020, 2 [²x dx '8 8 L³x dx - 30,…

A:

Q: x² = 2y²(y-1) y² = 2x²(x+1) x² = 2y²(y+1) y² = 2x²(x-1) dx (3x²-2-²) 4

A:

Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

A:

Q: 8 26 Type your answer without fractional or negative exponents. Use sqrt(x) for √√T. Find the…

A:

Q: To determine drug dosages, doctors estimate a person's body surface area (BSA) (in meters squared)…

A: To determine the drug usages, doctors estimate a person's body surface area BSA in meters squared…

Q: 1. Answer the questions below and then sketch the graph of the exponential function f(x) = (-)* + 1.…

A:

Q: Which one is correct for the sum of the geometric series O O O 9 10 11 5 17 10 6 5 O Divergent Σ1…

A:

Q: (1) Use the definition to prove that if x → 2 then (2x + 1)/x → 5/2.

A: xn→2 (2xn+1)xn

Q: adder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: The general term of the sequence is 2 -1 2 -1 2. - 1층글룸금.... 25 3 an = (-1)"+¹ ²1, n ≥ 1 (−1)²+12 n

A: Given :an=-1n+12n

Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 - 3t, where 0 ≤ t ≤ 0.5…

A:

Q: Let v = (2, -1, 5) and u = (5, -7,3). Find 37 - 5u

A: We have to find 3v - 5u

Q: Əw Find Ət using the appropriate Chain Rule for w = x² + y² + z² where x = 10rsin(s), y = 10tcos(s),…

A:

Q: If z = 5x2 + y2 and (x, y) changes from (1, 2) to (0.95, 2.1), compare the values of Δz and dz.…

A: We have to compare the values of Δz and dz.

Q: After receiving his first income, Mr. J invested P20,000 in a bank for his future family. The annual…

A: This question can be solved by applying the concept of compound interest.

Q: Find the derivative of f(x) = = 30 6/4x+1 Enclose numerators and denominators in parentheses. For…

A:

Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find f'(1). Note: Your answer (if it's not an integer)…

A:

Q: (5). a. The length of one side of a square tile is 1½ feet. Determine the area of the tile in square…

A:

Q: The function h(t) = ... gives the height from the ground of a ball thrown upwards. The time t is in…

A: We have to find the height when the ball is thrown, initial velocity, the average rate of change at…

Q: Find dw/ds and aw/at using the appropriate chain rule. Evaluate each partial derivative at given…

A:

Q: The limit is equal to 1312 Select one: O True O False lim n→∞ 3n 2n³ + 1

A:

Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface 2²-2y²-3²= -4…

A:

Q: The answer for x is correct but the answer for dy is wrong.

A:

Q: Calculate the accumulated amount of end-of-month payments of $9,000 made at 5.89% compounded…

A: The given data is: Monthly payement=$9,000Interest rare r=5.89%=0.0589Time t=5 years  Compounded…

Q: 6. Evaluate the following real integrals by residue theorem 3 •S 2 Vin H соз mx ~ (x²+a²) (x² + b²)…

A:

Q: f(x, y) = y^/x, P(1, 3), (a) Find the gradient of f. Vf(x, y) = = (21+ √51) U= (b) Evaluate the…

A: Topic:- application of derivatives

Q: the equation of the tangent line to the graph of the function f(x) = √√4x³ + 5 at V

A: Topic:- application of derivatives        Slope of tangent line is first derivatives of curve at…

Q: Find the exact sum of the following series 0 In ( ) 3 5 OH(-) - 12 (²³) In 3 (²/²) - ²3/ In 23 ○ In…

A:

Q: Find the average value have of the function h on the given interval. h(u) = (In(u))/u, [1, 6] have =…

A: The function is given as , hu=lnuu find the average value have on 1,6.

Q: 18x, x=2, AOR = X-AXIS

A: Topic:- application of integration

Q: Let f(x) be defined by f(x) = x² sin(x) + x³. Find f'(1). Note: Your answer (if it's not an integer)…

A: Please see the below picture for detailed solution.

Q: Graph the following function, showing all asymptotes and relative extreme points. 2x 16 x+4 f(x) =

A: The Solution is given below

Q: ven the vectors and w V (0,0) -5 -4 Q a) Sketch the vector 20 6 A -5 -4 -3 -2 -1 5 4 3 2 -1 V -2 -3…

A:

Q: 13. A certain type of glass is such that a slab 1" thick absorbs one-quarter of the light which…

A:

Q: a) (-²) lim x-0 3r b) = (₂) (72)" lim

A:

Q: Finding the Volume of a Solid. use the shell method to write and evaluate the definite integral that…

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Q: 13 Given Sine= - 12/23 and Cos0>0. Find the remaining trig. values of 0. From Sec 5.3

A: sinθ = -1/5 cosθ>0 here the quadrant given is 4th  because in 4th cosθ>0 and sinθ<0 now…