3) Given that f (x) = 2x + 8 g(x) = 5x – 2 / 4 and h(x) = 2x + 6 / X Find: - i) f (-5) = ii) g [f (0)] = iii) f [h (3)] =

Q: (2) Expand f(x) = cos x into a Taylor series centered at the origin (a = 0).

A: To expand fx=cos x into a Taylor series centered at the origin a=0.

Q: If ƒ(2) = 15, f' is continuous, and = the value of ƒ(6)? 6 [ f'(x) dx = 11,

A: Given query is to find the value of f(6).

Q: Use the Fundamental Theorem of Calculus to find •16 sin(x) S." dx =

A: Topic - Definite integral we are given, ∫116sinx4x34dxFormulas usedddxxn=nxn-1∫sin(x)dx=-cos(x)+C

Q: (1 point) Find the curvature (t) of the curve r(t) = (4 sin t)i + (4 sin t)j + (5 cost) k

A: we will find the required solution.

Q: 5. Use the Laplace transform to solve the initial value problem. y"+y'-2y=2e³, y(0)=-1, y'(0) = 4

A:

Q: A boat leaves a dock at 3:00 PM and travels due south at a speed of 20 km/h. Another boat has been…

A:

Q: a Evaluate the indefinite integrals the method of substitution using dx d) S e) 3 -x ³ 3+xx 1) 40…

A:

Q: I Evaluate Answer: sin(10x) cos(10x) dx.

A:

Q: A initial deposit in a bank account grows continuously according to the formula B=600e^.15t, where B…

A:

Q: A B C (D) (0, 2); Graph of f The graph of the function f shown above consists of two line segments.…

A:

Q: Use one-sided limits to determine whether the following limit exists and its value. If the limit…

A: Given:     limx→5x+6x-5 Left Hand Limit:    limx→5-x+6x-5   =limx→5-x+61x-5   For x approaching 5…

Q: 3 What is the book's definition of a smooth curve? Write down a pair of parametric equations for a…

A: Solve the following

Q: A bag contains 4 red marbles, 3 green marbles, 2 orange marble, 3 yellow marbles and 1 blue marble.…

A: Given information A bag contains 4 red marbles, 3 green marbles, 2 orange marble, 3 yellow marbles…

Q: Find the equation of the tangent line to the curve y = 8 sin z at the point The equation of this…

A: To find the equation of the tangent line to the curve y=8 sin x at the point π6, 4.

Q: Laptop computers are measured according to the diagonals of their screens. A 18-inch laptop has a…

A:

Q: c) O 28T d) 112T e) ○ 56T f) O None of these. I

A:

Q: and find If 4 6 √ ² = 4 f(x) dx 25 LIAS g(x) dx = 9, [4f(x) — 3g(x)]dx.

A:

Q: Suppose we have the following Production Function: Q = L^0.25 K^0.75 Calculate the Marginal…

A:

Q: Answer: If f is continuous and [10 *f(t) dt = 12, find the integral [*²1² ƒ (1³) di dt.

A:

Q: Setup the Riemann sum n ['so k=1 f(x) dx : = •5 x³ dx = lim ((2+3/nk)^3)*(3/n) n→∞ n lim f(x)Ax for…

A: Riemann sum of ∫abf(x)=limn->∞∑k=1nf(xi)∆x, where ∆x=(b-a)/n

Q: Question 3 Given the demand function D(p) Find the Elasticity of Demand at a price of $105 Raise…

A:

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

A: We have to find the distance between 12:00pm and 2:30pm.

Q: In(a/b) = ln(a) — In(b) for all a, b>0 -- O True O False

A: See this solution in below.

Q: (1 point) (a) Check all of the following that are true for the series Σ n=1 3" 2"-1 OA. This series…

A:

Q: (a) Compute 83 of ∞ (c) Use n = 3 and n=1 2 9n6 (b) Estimate the error in using $3 as an…

A:

Q: Question 4 Solve the differential equation. 6y¹ = ex/6 + y A) y = B) y = E xex/6 + cex/6 6 Ⓒy=xex/6…

A:

Q: Find the slope of the tangent line to the curve 2xy - 3y³ = -9 - -4x² - at the point (2, -1).

A: NOTE: Refresh your page if you can't see any equations. . the given curve is  and the given point…

Q: Let f(x) = = f'(x) = - 2 log(x) ƒ' (5) Round to 4 decimal places if needed. =

A:

Q: Evaluate the following limit. Enter an exact numeric answer. To enter ∞o in your answer field, •…

A:

Q: List the first five terms of the sequence. a₁ = 5, an+ 1 al a2 a3 a 4 = = || || III = 2an +2

A: given  an+1=2an+2for a2 put n=1a1+1=2a1+2given a1=5

Q: Find the dimensions of a rectangle (in m) with perimeter 68 m whose area is as large as possible.…

A: NOTE: Refresh your page if you can't see any equations. . x=width of the rectangle y=length of the…

Q: A forest fire is found at midnight. It covers 1200 acres then. It is spreading at a rate of f(t) =…

A:

Q: 3-t Let F(x) = √² + 40 (a) Find the value of a where F obtains its maximum value. x = dt for -∞0 < x…

A:

Q: L₂ (x + 2)ex²+4x+3 dx -2 =

A: Given: I=∫-20x+2ex2+4x+3dx    ....1   As we know the common integral, ∫exdx=ex+C   Note: As per…

Q: Determine the limit given that A, B, C, a, b, c ER (they are elements of the set of real numbers).…

A:

Q: ÿ M J +.1.0. = 40.CO.sx...

A: We need to solve Differential equation.

Q: A forest fire is found at midnight. It covers 1000 acres then. It is spreading at a rate of f(t) =…

A: Initially at time (t=0)  area covered by fire is =1000 acres Rate of spread =4t12   You'll have to…

Q: Evaluate the integral. o x sin x sin(x) cos(x) dx

A:

Q: Question 9 Solve the differential equation. y'e³x + 3ye³x = 4x A) y = 4x²e3x + ce³x B) y = 4x²e-3x +…

A: Topic = Differential Equation Correct Option = C

Q: Given ƒ(x) = √² t² - 49 1 + cos² (t) At what value of x does the local max of f(x) occur? x = dt

A: We have to find the local max of f(x).

Q: g(1) = g(2) = g(3) = g(6) = B. On what open interval(s) is g increasing? C. At what value of x on…

A:

Q: Find an equation of the line tangent to the graph of f(x)=x3 at (1,1).

A: Find an equation of the line tangent to the graph of   f(x)=x3 at (1,1).

Q: Use linear approximation, i.e. the tangent line, to approximate √49.2. Let f(x) = √√x. A. Find the…

A: As per bartleby  guidelines only one question is allowed to solve if multiple question is asked in…

Q: Find the critical points of f(x) = 2 cos (3x) + 3 cos (2x) in [−3ñ, −ñ]. (Give your answer in the…

A: Given: fx=2cos3x+3cos2x  To find: Critical points of f(x) in -3π,-π Critical points of a function…

Q: Evaluate the limit, using L'Hopital's Rule. 3 lim (1+4x) x+0+ =

A:

Q: 10y=10sin(pi(x-5))+40 find midline

A: note - midline is the line which runs between maximum and minimum value standard form y = asin( bx +…

Q: Use Newton's method to find all real roots of the equation correct to six decimal places. (Enter…

A: Given 2x=1+x3. This can be written as fx=x3-2x+1. Now,  f'x=3x2+2x2 Now, consider: When x=-1, then ,…

Q: Consider a right triangle with a side of length z opposite angle A, a side of length y opposite…

A:

Q: Find the distance between the two points shown below. A -6 -5 -4 -3 -2 Distance = -1 4 3 2 1 -1 -2 1…

A: we will find the required.

Q: Diff eqn. 25) y' + (tan x)y = cos x when -pi/2 < x < pi/2

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have