Cash has available 1200 yards of fencing and wishes to enclose a rectangular area. ​(a) Express the area A of the rectangle as a function of the width W of the rectangle. ​(b) For what value of W is the area largest? ​(c) What is the maximum area?

Q: Evaluate h'(4) where h(x) = f(x) · g(x) given the following. • f(4) = 7 • f '(4) = −2.5…

A: Given h( x ) = f( x ).g( x ) as we know that ddx( u.v ) = udvdx + vdudxGiven f( 4 ) = 7 f'( 4 ) =…

Q: Find the volume of the region cut from the solid cylinder x² + y² ≤ 1 by the sphere x² + y² + z² =…

A:

Q: Let F(t) = Find a parametric equation of the line tangent to r(t) at the point (157, 16, 4.159)…

A:

Q: 3. The figure below shows the graph of the derivative of f'(x). Use this to determine the location…

A:

Q: Let F(t) = (-t² + 3, e-3t, - 2 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 -

A:

Q: Express the equation in exponential form (a) log₂ 8 = 3. That is, write your answer in the form 24 =…

A:

Q: Using the graph of the function H(x) below, find the following. 10+ -10 Evaluate -10+ 7 SH(x) dx = 1…

A:

Q: Find the area of the region enclosed by f(x) and the​ x-axis for the given function over the…

A:

Q: Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE.) 9x³…

A: We have to find asymptotes.

Q: function f is (-7,-3) and the range of f is 0,5, state the domain and range of f^(-1).

A: Here domain of f is (-7, -3) and range of f is (0,5) To determine domain and rang of f^(-1)

Q: Find the following limit. lim

A: limt→32t2+t-5,t2+2t-15t-3,3·cost

Q: The following limit represent the derivative of a function f at a point a. Find a possible f and a,…

A: let function is f(x) given is derivative f'(x)=limh→0(1hsin2(π4+h)-12

Q: The total cost of producing 1 unit of a product is given by C(x, y) = 90+ 0.3x² + 60y - xy dollars…

A: The total cost of producing 1 unit of a product is given by C( x , y ) = 90 + 0.3x2 + 60y - xy…

Q: . (Section 14.4) Let curve C be described by vector function(t) = (cost-1, sint, 3/2) on 0 ≤ t ≤ b.…

A: We have to find the value of b so that the length of the curve is 18 units

Q: Consider the following. 16x8 x² +1 Determine the value that the function f approaches as the…

A:

Q: exact location of all the relative and absolute g(t)=87t^(4)-464t^(3)+696t^(2)+29 with dt

A: Consider the given function. gt=87t4-464t3+696t2+29

Q: Use the tabulated values of f to evaluate the left and right Riemann sums for n = 10 over the…

A:

Q: Use the appropriate methods to solve the following integrals. e² +€0.5€ e²x a. So - dx

A: By using the appropriate method to solve the following integral. ∫01ex+e0.5xe2x dx

Q: Use the power series ∞ 1 1 + x = Σ (-1)"x", |×| < 1 n = 0 to find a power series for the function,…

A: NOTE: Refresh your page if you can't see any equations. . it is given that, . substitute x=0

Q: Consider the following functions. f(x) = 5x and g(x) = √√√√x-1 Step 1 of 2: Find the formula for (f…

A:

Q: Find the area of the region bounded by the curves x4- 9x2 and xx3 - 9x between −3 ≤ x ≤ 3. Show all…

A:

Q: If f (x) = ln x, then lim I-3 А B D In 3 nonexistent f(x)-f(3) is

A:

Q: K Find the area under the given curve over the indicated interval. y = 2x; [1,4] The area under the…

A: Given function y=2x ,and x belong to x=1 to x=4

Q: Find the length of the curve r(t) = (5 cos(2t), 5 sin(2t), 2t) for − 2 ≤ t ≤ Give your answer to two…

A:

Q: Find the interest rate needed for an investment of $5000 to grow to an amount of $9500 in 4 years if…

A:

Q: K Identify the inflection points and local maxima and minima of the graphed function. Identify the…

A:

Q: Evaluate the limit. Lim (x,y) → (0,0) 3x³ +5y² 2x² - y²

A:

Q: write a rational expression with the following restrictions = x=0,8,-(4)/(5)

A:

Q: Convert the point (r, 0, z) = (6, 7, 4) to Cartesian coordinates. Give answers either as…

A:

Q: (5) Determine the intervals on which the graph is concave upward or downward. Find the inflection(s)…

A: fx=-x3+6x2-9x-1

Q: in a form with no logarithm of a product, quotient or power. After rewriting we have with A = B =…

A:

Q: Find the area of region A in Figure 6. G FIGURE 6 F:r = 16 cos 0, Tg = 1, F 2rx G:r = 1 rf = 8

A:

Q: Let f(x) = Then f'(x) b = 9 sin x 4 sin x + 2 cos x = 9/(2(2sin(x)+ cos(x))^2) The equation of the…

A:

Q: Evaluate the following limit using L'Hospital's rule. lim x→∞ ln(x3) / ( 4√(2x+5))

A:

Q: Using the graph below, estimate the magnitude of the error in approximating sin x by x for -1.3 ≤ x…

A: We have to estimate the magnitude of the error in approximating sin x by x for -1.3≤x≤1.3.

Q: a. Solve the system u = 2x + 3y, v=x+4y for x and y in terms of u and v. Then find the value of the…

A:

Q: Find the volume of the solid

A: Z = x2 + y2  And z = 27 - 2x2 - 2y2  Find the volume of the solid bounded by the curve.

Q: Find the average value over the given interval. y=9e *; [0,1] The average value is (Type an exact…

A:

Q: The concentration, C, of phenylbutazone, in micrograms per milliliter (µg/mL), in the plasma of a…

A:

Q: Let F(t) = Find 7' (t) 7' (t) =< Calculator Check Answer

A:

Q: Find the angle between v and w if v . w = ✓ ||v|| . ||w||. (Use symbolic notation and fractions…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Convert the point (x, y, z) = (-2, 1, 0) to cylindrical coordinates. Give answers as pos values,…

A: given point is  :-x,y,z =-2,-1,0then we have to convert it  into  cylindrical  coordinates

Q: Calculate R8 for f(x) = 10 − x over [3, 5]. R8

A: f(x)= 10-x Over [3,5] We have to calculate R8

Q: The expression (3/1/5) 3/5 equals y where r, the exponent of y, is:

A:

Q: find the equation on a straight line m=4 passing through 2,7

A: Equation of line passing through point x1,y1 and slope m⇒y-y1=mx-x1

Q: 16. Of all numbers whose sum is 340, find the two that have the maximum product. A. 10 and 330 B.…

A: Let one number be x and the other number y, then                x+y= 340       ⇒  y=340-x…

Q: Use the model for projectile motion, assuming there is no air resistance. Determine the maximum…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Consider the following function. (If an answer does not exist, enter DNE.) 3 f(x) = 1 + X= X (a)…

A:

Q: Given that y₁ and y2 are linearly independent solutions to the differential equation, state the…

A: Given linearly independent solutions are: y1=excos(2x)y2=exsin(2x)

Q: 4 3 2 a 155 + To find the blue shaded area above, we would calculate: [ f(x) dx = area Where: f(x) =

A: