The figure shows how a function f(x) and its linear approximation (i.e., its tangent line) change value when a changes from co to xo + da. Suppose f(x) = x² + 2x, xo = 1 and dx = 0.05. Your answers below need to be very precise, so use many decimal places. (a) Find the change Af = f(xo + da) - f(xo). Af=0 (b) Find the estimate (i.e., the differential) df = f'(ro) dx. df = (c) Find the approximation error | Af-df. Error = f(xo + dr) f(ro) Af = f(zo + dz)-f(zo) dz v=f(x) Error-Af-df Zo (Click on graph to enlarge) df-f(z)dz to + dz Tangent

Q: Question 3.52) Consider the curves y = f(x)=x² and y= g(x)=(x-2)² -2. Find the acute angle of…

A: Set the two functions equal to each other and solve for x:x^2 = (x - 2)^2 - 2Expand and simplify the…

Q: Write the integral as the sum of the integral of an odd function and the integral of an even…

A:

Q: Find the point at which the line {-1,-3,-5} + t{5,-3,3} intersects the plane 4x-y-z= 104

A:

Q: The manager of a 100-unit apartment complex knows from experience that all units will be occupied if…

A: Find maximum  revenue, what rent should manager charge and the variable used to find the maximum…

Q: Find the derivative of the function. v(x) = e2x52x v'(x) = X

A:

Q: Find the area of the region bounded by the hyperbola 92² - 4y² = 36 and the line x = 3.

A:

Q: Consider the plane which passes through the three points: (3,-2,-10), (-2, 2, 6), and (-2, 3, -4).…

A:

Q: Convert the point from spherical coordinates to rectangular coordinates. π (8, 2, 4) ( [ (x, y, z)=

A: In this question, we will convert the point from spherical coordinates to rectangular coordinates.

Q: 2. About the x-axis y = √√x (4,2) y=x

A:

Q: Find the approximations Tn Mn and S, for n = 6 and 12. Then compute the corresponding errors E, EM…

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. (If an answer does…

A: we are given the function and we need to find out the absolute extrema in the given interval.

Q: Let g(x) = f(t) dt where fis the function whose graph is shown in the figure. y f LA t 1 2 3 4 5 6 7…

A:

Q: Let ✈ denote the vector xỉ + y j + z k and a be a fixed positive constant. Compute divF where is the…

A: Let  denote the vector  and  be a fixed positive constant.To compute where  is the vector field…

Q: Graph the following quadratic function: f(x)=x²-8x+12 Along with the graph, provide the following: •…

A:

Q: Determine whether the series is convergent or divergent. 3 1 3 + + 16 32 64 1 3 2 + + + 4 8 O…

A:

Q: If the nth partial sum of a series an is n = 1 Sn a 1 = 00 Find an and Ear an n = 1 an Σ an n = 1 =…

A:

Q: Suppose it is know that the function f(x) = has a maximum value of 2 attained at x = 6. Can you…

A:

Q: Simplify the expression to a + bi form: (8 + 3i)(4 + 4i)

A:

Q: f(t) = 2t³ + 3t2 - 36t

A:

Q: Let y = f(x) be given by the graph below: -6 -5 Not Image 0-4 0-1 02 -4 04 -3 -2 -1 6 1 -1 -2H -31…

A: A graph of the function is given.The aim is to find the points at which the function is left…

Q: USE THE RATIO TEST TO DETERMINE WHETHER & n(-9)h n=29 n! CONVERGES OR DIVERGES. FIND THE RATIO OF…

A:

Q: A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: Find an equation for the conic that satisfies the given conditions. parabola, focus (-10, 0),…

A: Focus : Directrix:  x=2

Q: 2. Find the critical numbers and the open intervals on which the function is increasing or…

A:

Q: Settings es Problems plem 1 ✓ Previous Problem Problem List (1 point) Evaluate the triple integral…

A: The objective of this question is to evaluate the triple integral of the function xy over the solid…

Q: Express the point given in Cartesian coordinates in cylindrical coordinates (r, 0, z). A) (³ ( ¹⁄²),…

A:

Q: Use the table of values for the functions p(x) and g(x) below to complete the tables for the…

A: Note: As per our guidelines, we can solve first question. Please repost remaining questions.

Q: Which linear function is represented by the standard form equation below? 4x + 5y=40 A f(x) = -x+8 B…

A: the standard form of equation is 4x+5y=40

Q: Let lim g(x) = -1 and lim h(x) = 10 x 4 x→4 Determine the value of the limit lim [8+√xh(x) x→4

A: Let, To determine the value of the following limit.

Q: Let f be a differentiable function such that ƒ (3) = 15, ƒ (6) = 3, ƒ′ (3) = −8, and f' (6) = -2.The…

A:

Q: Find the general solution except when the exercise stipulates otherwise. (D2-1)y=0; when x=0, y=y0,…

A: find the general solution of the

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: Consider the function

Q: The cost of manufacturing a toasters in one day is given by (A) Find the average cost function C(x).…

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

Q: Find the length of the curve y = 5+³/2, 0≤x≤ 2. [Formula you may need: arc length formula L = - S*…

A: Formula for the length of the curve is given as follows

Q: k nverge or diverge?

A:

Q: Use the chain rule to find the derivative of f(x) =6√/9x³ +8x6 Type your answer without fractional…

A:

Q: Consider the indefinite integral The integrand decomposes into the form ax + b + where a = b = C =…

A:

Q: M8 n=1 4 (4n – 3)(4n + 1)

A:

Q: Long-Term Investments   This exercise is based on the following table, which lists interest rates on…

A:

Q: A rectangular area adjacent to a river is fenced​ in; no fence is needed on the river side. The…

A: A rectangular area adjacent to a river is fenced​ in; no fence is needed on the river side. The…

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A:

Q: DECIDE WHETHER THE GIVEN SEQUENCE OR SERIES IS CONVERGENT OR DIVERGENT. IF CONVERGENT, ENTER THE…

A:

Q: ints) Determine if the improper integral is convergent or divergent. Eval- e integral if it is…

A:

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Given,Area of a triangle, =88 Altitude of a triangle, The rate of increase of altitude of a…

Q: the integral if it is convergent. foo Ind x5 In(x) dx divergent. Evaluate

A:

Q: X 0 f(x) 3 f'(x) 4 042 1 5 -1 1 273 2 7 362 4 1 X 2 3 4 g(x) 3 0 7 2 g'(x) 2 4 -3 -2 3 5 2 5 0 -2 5…

A:

Q: Use Cramer's Rule to solve: (x + 7y=23 (6x+y=15

A:

Q: Let f be the function below. Indicate where f(x) is differentiable. You may click on the graph to…

A:

Q: Oil has spilled in the ocean. The volume of oil in a spill in the shape of a cylinder of height 6…

A:

Q: Evaluate using trigonometric substitution. Refer to the table of trigonometric integrals as…

A: