If possible, find the number k so that f is continuous at every point. 3x+3, x<-2 f(x)= kx+6, x≥-2

Q: Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and…

A: The given total inventory cost function

Q: Show that the function (f : [0, infinity) -> R given by f(x) = e^{2x} - 2e^x + 2 ] has an inverse…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: y= (2+6 times x)^x Use Logarithmic Differentiation to find dy/dx

A: Conclusion :  dxdy​=(2+6x)x [(2+6x)6x​+log(2+6x)]Explanation:Step 1: Approach 1 ) Take both side…

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: To find the volume of the solid that results when the shaded region is revolved about the indicated…

Q: Use the Chain Rule to find the indicated partial derivatives. = x² + x²y, x = s +2tu, y = stu²; Z =…

A:

Q: The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The…

A: Please see the explanation Explanation:Step 1:

Q: Which of the following lines is perpendicular to the line (10,-6,-3)+s(1,2,-2), s ER - b.…

A: 1. Option (d) 2. Option (c) Explanation:Step 1: Step 2: Step 3: Step 4:

Q: In this problem, p is in dollars and x is the number of units. The demand function for a certain…

A: Thus, the equilibrium point is (x,p)=(3,112).The consumer's surplus at the equilibrium point is…

Q: Give an example of a divergent alternating series satisfying only Condition (ii) of the Leibniz…

A: ∑n=1∞​(−1)nn+2n​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: The volume, V cm³, of a sphere is given by 4 V = πr³ where r is its radius. 3 It is given that the…

A: Answer: 640Explanation:

Q: y = 1x312, 0 ≤ x ≤ 21

A:

Q: please solve this

A: Ans :  Volume = 2.24 cubic units ( approximating upto 2 decimal places)Explanation:Explaination:

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.05t³ +…

A: Answers :: Part -&gt; (A)S′(t)=0.15t2+1.6t+3 Part -&gt; (B)S(6)=66.6S′(6)=18Explanation:Sol)

Q: e^0.006x= 25 = 536.48 what is 536.48 rounded to four decimal places?

A: Answer : 536.4793  (Rounded to four decimal places)Explanation: Given,  e0.006x=25 Logarithm on both…

Q: In this problem, p is in dollars and x is the number of units. If the supply function for a…

A: 996Explanation:Detailed explanation:

Q: Calculate the derivative of the following function. y = (x²+3x-2) dy dx

A:

Q: Please review and solve problem 6 part 'a' and 'b' and explain how the answer was found. Problem…

A: The answers are attached.Explanation:Step 1:

Q: 0 and x = The curve y = 9√√√ is rotated about the x-axis between x = : 1 through an angle of 2…

A: ans=40.99 pie sq unitsExplanation:

Q: #1: For which of the cases below do the given functions form a fundamental set of solutions of the…

A: Summary: - (i) does not form a fundamental set due to missing different exponent solutions and…

Q: Find the first partial derivatives of the function 5x f(x, y) = (x + y)²° 1. fx(x, y) = 2. fy(x, y)…

A: 1.fx​(x,y)=(x+y)35y−5x​ 2.fy​(x,y)=(x+y)3−10x​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Use the One to One Property of Exponentiation to solve the following exponential equation. Input…

A: 23x= 41+xWe have to find value of x using one to one property of exponential

Q: Need help with A and B of this equation

A: (A) N′(x)=x23630​ (B) N′(10)=36.3At $10,000 level of advertising, sales are increasing at the rate…

Q: Use the graph to evaluate the limit. lim f(x) 0+x -B 6 30 2 R X +30 G OA. -3 OB. 3 ○ C. 0 OD. The…

A:

Q: Find dy/dx and dx/dy from 6x2-x³y²+4x=0

A:

Q: Prove that 3 is prime.

A:

Q: Find the volume of the solid generated when the region enclosed by √√√x, y = 6 — x, and y: 0 is…

A: y =√xy=6-xy=0 revolved about the x-axis

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.…

A: The rate at which the volume of the snowball is decreasing (due to the negative value of dv/dt) when…

Q: Find the first partial derivatives of the function. მu მr = მ მყ u = ln(x + 5y + 6:) მ:

A: Solution of the above mentioned problem is provided below for further queries u may ask in comments…

Q: dy Find dx x=8e8 y = e 010

A:

Q: iv. Σ n=1 40n (2n-1)2 (2n+1)2

A: The given series

Q: Write the corresponding rectangular equation for the curve represented by the parametric equation…

A:

Q: Find the volume of revolution by rotating the region bounded by y=4^x, y=0,x=0,x=2 about the line…

A: Region is bounded by y=4x,y=0,x=0,x=2Rotating the region about y=−1Using the washer method

Q: 2x-3 Draw a graph of f(x): == +1 by first placing the horizontal and vertical asymptotes, then…

A: The given function

Q: 2) The contour map of f(x, y) is shown below. Use it to find fx (1,3) 10 10 8 8 6 =2 6 0 x=2 6 8 10

A: fx​(1,3)=1   Explanation:From the given contour map, we can see that, f(1,3)=4  Similarly we can…

Q: help

A: So, the consumer's surplus is $30.Explanation:To find the consumer's surplus, we first need to find…

Q: imit: 6-xy lim (x,y)-(2,2) x²+2y²

A:

Q: 1. Evaluate each of the following integrals. If partial fraction decomposition of the rational…

A:

Q: Find the derivative of y = cos A with respect to x. The derivative of y = cos ( 0- with respect to x…

A:

Q: If 0=28°, find the distance between two cities, A and B, to the nearest mile. The radius of the…

A: The objective of this question is to find the distance between two cities, A and B, given the angle…

Q: You should have observed that the general pattern using the fractional format is: 2n 8642 I(n) = 2…

A: We have given a series I(n)We have to observe and rewrite in general pattern

Q: Use a sketch to find the exact value of the following expression. tan cos 10 26 Which of the…

A: Answer:Option C. The correct triangle to find the value of the expression is Option C. Here's…

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), e" + cos(v)). Use…

A: Answer:  gu​(0,0)=17gv​(0,0)=8Explanation:Step 1:

Q: Please don't provide handwritten solution ...

A: The objective of the question is to find the intersection points of the given equations.

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Angle that vector a = (12,-3,4) makes with the y-axis is  arccos(13−3​)Explanation: For any query…

Q: Let (f : [0, infinity) -&gt; R be an arbitrary continuous function, which is differentiable on…

A: The objective of this question is to prove that for a given function f, which is continuous and…

Q: The point (1,1,1) is connected to the origin by a curve, C, formed by the union of two lines: the…

A: The objective of the question is to find the parametric representation of the second part of the…

Q: Find an equation of the ellipse with vertices (0, 3), (12, 3) and eccentricity e = Select one: a.…

A: Vertices:eccentricity, e=

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: The answers are as follows: 7.The vector equation of the line isr=(7,2)+s(2,−3),s∈R.Option b. is…

Q: Find a vector perpendicular to both a = [1,2,3] and b = [4,2,-3].

A: Answer is given below :-Explanation:

Q: The accompanying figure shows the dimensions of a light bulb at 10 equally spaced points. 1.60 3.20…

A: