Suppose f(4) = -1 and f'(4) = -10. An object moves along the curve y³ - 2x² f(x) - 2x = 51. For a final project at North Carolina State University, Kayden needs the equation of the line tangent to the curve at the point where x = 4. The eqution of the tangent line needed by Kayden is

Q: The demand curve for a certain product is given by p(q)=567−q2. The supply curve is given by…

A:

Q: Find a parametric representation for the surface. the part of the cylinder x² + z² = 16 that lies…

A:

Q: Question 8 What is the 9th term of the sequence a ¹ = ( − 1)²″ (n − 10),

A:

Q: For the given function, determine the following if possible. If it is not possible, explain why. You…

A: .

Q: A norman window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the…

A:

Q: When we estimate distances from velocity data, it is sometimes necessary to use times to, t₁, t₂,…

A:

Q: 1-4 The graph of the derivative f' of a function f is shown. (a) On what intervals is f increasing?…

A: Note: Concepts: 1. Function f(x) is increasing where f'(x)>0 2. Function f(x) is decreasing…

Q: Calculate the area of the surface obtained by rotating the curve of the following function about the…

A: The given surface is:y=x+3      with 0≤x≤1

Q: charge is distributed over the triangular region D shown below so that the charge density a (x, y)…

A: We are given with the triangular region  D so that charge density at (x,y) isσ(x,y)= 4xy  To find:…

Q: 1. slope = 5. slope 2. slope -34 2 = AIG 4 3. slope = -1 I 4. slope = = 2 3 4 Find the slope of the…

A:

Q: if y=2u^4-4(u^2-2u)^2 and u=√x-1 find dy/dx when x=10

A:

Q: lim X→18 V 1 + 16x6 5-x³ +3

A: We know that the value 1/infinity=0

Q: K Find or approximate all points at which the given function equals its average value on the given…

A: f(x)=-(π/4)sinx  on interval [-π,0]

Q: valuate √ F. dĩ where F =, and C' is given by F(t) =, 0≤ t ≤

A: Firs change x=t4,y=t,z=2 then find integral

Q: For the parametric curve defined by x(t) = 4cos²t, y(t) = 4sin²t. Part A: For the given parametric…

A:

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 9…

A:

Q: Question 4 Let y = (x² − 1)³(e³ª + x²)-². Then equals a) 3₁-3-² (b) 31- 3e³x +2x e³x+x² (c)…

A:

Q: Given the following limits, lim f(x)=0; lim g(x)=0; lim h(x)=1; lim p(x)=0; lim q(x)=0⁰ x→a x→a x→a…

A:

Q: Find the equation of the horizontal asymptote of the function f(x)=- (2x+5) Oy= 64 f(x) has no…

A:

Q: 6) The base of the solid is the disk x2 + y2 ≤36. The cross sections by planes perpendicular to the…

A:

Q: If a supply curve is modeled by the equation p= 200+ 0.2q3/2, find the producer surplus when the…

A:

Q: Find the equation of the horizontal asymptote of the function gx2x²+7x+3 5x² O O f(x) has no…

A:

Q: Question 9 Suppose that f'(t) > −3 for all t € R and ƒ(3) = −1. Then ƒ(−7) is (a) > 29 (b) 31 (e)…

A:

Q: 43. 2+√4-x²-y² BS 2²/ -2 -√√4-x 2-√4-x²-y2 (x² + y² + z²)³/2 dz dy dx

A:

Q: Jo F. dr where C is oriented counterclockwise as viewed from above. Use Stokes' Theorem to evaluate…

A:

Q: Ga Time (h) Text messages 0 25 65 Cost ($) 0 5 13 3. Andy's text plan for his cellphone is shown in…

A: (a) to draw a graph. (b) slope, m = ? & what does it mean?

Q: y = f(x) 4.

A:

Q: (:((: Need nea

A: The expression is given as  7x+1-7x.Simplifying the…

Q: What is the area of the integral of f(x) = 2within the interval [1, 4]? 3 2.5- 2 1.5+ 1 0.5 0 1 2 3…

A:

Q: Find the area of the region that lies inside the first curve and outside the second curve =32…

A: r2=32cos2θr=4

Q: Identify the surface by eliminating the parameters from the vector-value r(u.v) = 3 cosv cosui +3…

A:

Q: What formula would be used to calculate the left rectangle approximation of cos x sin x dx using…

A: △x=2-05=0.4Endpoints0 , 0.4 , 0.8 , 1.2 , 1.6 , 2

Q: Find √√3 x² +3 x² +1 dx

A:

Q: Consider the function f(x) = 4 - 2x², - 5 ≤ x ≤ 2. The absolute maximum value is and this occurs at…

A: given,  f(x)=4-2x2,  -5≤x≤2

Q: Write the equation log_(243)729=(6)/(5) in exponential form.

A: log243729=65

Q: Solve the differential equation. 7√xy dx = 1, dy dx x, y>0

A:

Q: Calculate the work W against gravity required to build a box of height 7 m and a square base of side…

A: Given a box of height 7m and a square base of side 3m out of a lightweight material of density 600…

Q: The cost, in dollars, to produce a vats of ice cream is C'(x) = 8x + 6. When selling them to ice…

A:

Q: Find the slope and concavity of the parametric curve at the point t = (1/2), x(t) = (1/2)t² -1,…

A: To find the slope of the curve at t = 1/2, we need to find the derivative of y with respect to x:…

Q: Find the total mass of the wire with density P. 8 (t) = 1² +21), p(x,y) = y,0 st≤1

A:

Q: A wall "h" meters high is 2 m away from the building. The shortest ladder that can reach the…

A: Note:- Since you asked multiple questions ,according to our policy we can solve only first question…

Q: Sect - tant = sect + tant

A: let  H=sec(t)-tan(t)

Q: Calculate the exact area bounded by the Kaxis and the graph y=15-8x+x². area=

A: At x-axis, the value of y is 0. y=15-8x+x2=0x2-8x+15=0x2-5x-3x+15=0x(x-5)-3(x-5)=0(x-3)(x-5)=0x-3=0…

Q: Question 5 If y = (sin x)", then dy (a) g[ln(sinx) +cot] (e) none of these (b) y[ln(sin x) + cot x]…

A: Given: y=(sinx)x We have to find dy/dx

Q: Use the product rule to find the derivative of j(x) = (4x³) (2x² − 3). If we set f(x) ƒ'(x) g'(x)…

A:

Q: b b [ 2² dx = 4 ve [dz = 3 dx α a

A:

Q: R is the region bounded by the functions f(x) = -4-7 and g(x) = -4 over the interval [a, b] where a…

A: To find out the area of the shaded region.

Q: Find the derivative off when f(x) = 6x + +6π. 4 x3

A: Find the derivative of f when       fx=6x4+4x3+6π

Q: Can someone help me with this please?

A:

Q: f(x) = (6x2-4)7(-3x2+3)13 f'(x)=

A: