Suppose y = √2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dy X dt = (b) If dy/dt = 3, find dx/dt when x = 40. dx = dt

Q: A typical dish antenna is built as a surface of revolution obtained by revolving a parabola about an…

A: We to find the surface area of the surface in terms of R and K

Q: √ x2 (4x² + x² − 1) ³. Find the derivative of f (x) = =

A:

Q: +9.25 where A(t) represents the 1. Jacy keeps track of the amount of average monthly rainfall in her…

A:

Q: (a) ( Find an equation of the sphere that passes through the point (-3, 3, -2) and centered at the…

A: We have to find the equation of the sphere that passes through the point (-3,3,-2) and centered at…

Q: Derive the volume formula of the cone by integration. In doing so, (a) find the equation of the line…

A:

Q: Find an equation of the tangent plane to the surface at the g h(x, y) = In √√x² + y², (6, 8, In 10)

A: Given: h(x,y)=lnx2+y2  at (6,8, ln10) To find: The equation of the plane to the surface

Q: y 2 y = f'(x) 4 6 x

A: here , we have graph of the derivative of function  f means  f' :-then finding following :-(a)…

Q: x3 The function f is defined by f(x) = x-2 Find the x-coordinates of all local extreme values of f.

A:

Q: You are standing above the point (2, 2) on the surface z = 15 - (3x² + 2y²). (a) In which direction…

A: Please see the below picture for detailed solution.

Q: Is it possible to answer this using factoring, conjugate or any alternative methods? If so, could…

A: To evaluate the following limit. limx→0 x+13-1x

Q: 1. For the function y = 2x²-3x use a simplified algebraic expression in terms of a and h to estimate…

A:

Q: Locate the critical points of the following function. Then use the Second Derivative Test to…

A: The given function is;  f(x)=-x3+15x2.

Q: List all of the possible rational zeros for the function f(x) = 4x² − 3x³ + x² − 6 H Normal Enter…

A:

Q: Use the given feasible region determined by the constraint inequalities to find the maximum and…

A: For finding maximum and minimum value of the given function we need to check at every given point…

Q: If g(x)=√1+tdt, then find the derivative g'(x).

A: Given :- gx=∫0sinx1+tdt

Q: An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will minimize…

A: Let the base height and length be x and the height be y.Given: the volume is 4 cubic feet.

Q: Question 2 of 10 Determine whether the equation is a conditional equation, an identity, or a…

A:

Q: Find a plane containing the point (1,4,3) and the line of of the planes 7x + 5y - 8z = 27 and 5x +…

A:

Q: For the equation, use implicit differentiation to find  dy dx. (x − 3)(y − 3) = 4

A: Given query is to find derivative.

Q: 5. area A of the surface generated by rotating the region R about the line y = -3. Let R be the…

A:

Q: da x²√4x-9 dt Ive²-√t dx X- - √√x

A: We can solve this integral using substitution. Let's make the substitution u = 4x - 9. Then du/dx =…

Q: Find all critical points of the following functions. a. f(x) = -r² + 10x + 43 b. g(x) = ¹/3 c. h(r)…

A: To find the critical points for given function

Q: Find the limit. lim (csc (2x) - cot (2x) + cos (4x)) = (Type an exact answer.) X→0*

A:

Q: sing the following graph of the function f, aluate the limits (a) through (i). 10 -2 8t 6- -2 -4 y X…

A:

Q: (a) Use the definition given below with right endpoints to express the area under the curve y = x³…

A:

Q: The table below shows the value, V, of an investment (in dollars) after n years. n 3 7 12 14 19 0…

A: Solution: By using exponential regression graph plotter

Q: Volume = --1 1,0

A:

Q: 1. Find the linearization of f(x) = (x³ + 1)¹/² at x = 2 and use this to estimate f(2.05).

A: Please see the below picture for detailed solution.

Q: 1) ƒ(2) = ƒ(4)=0 max /mm f(3) is defined f'(x) 0 on (3,∞) inc f'(3) is undefined f"(x) < 0 if x #3

A: We have to Sketch a graph of this function based on the info given.

Q: x(t) Find the point at which the line y(t) z(t) = = = 4 - 8t -4+ 5t intersects the yz plane. 6 + 2t

A:

Q: 3. Let f(x,y)=x²y/(x² + y²). (a) Show that f(x,y) goes to zero if (x,y) goes to (0,0) along any…

A: Solution: (a) If (x,y) approaches (0,0) along the straight line y = mx, then we can substitute mx…

Q: Find equations of the tangent lines to the curve x-1 x + 1 that are parallel to the line x - 2y = 3.…

A: Given  curve equation:- y=x-1x+1

Q: Find the average height of the paraboloid z = x² + y² over the square 0≤x≤3, 0≤ y ≤3. The average…

A: Given data The equation of paraboloid is, z=x2+y2. The limits of the square is 0≤x≤3, 0≤y≤3.

Q: 5. Consider a unit vector u = (a,b). (a) How many unit vectors are orthogonal to u? (b) Explain a…

A:

Q: 3. Identify the graph of f(x,y)=x²-x+3y² +12y-13, state where it attains its minimum value, and find…

A:

Q: car leaves the city traveling north at a constant speed of 60 miles per hour. A second car leaves at…

A: The details solution of the given question is given below in step 2.

Q: The trough in the figure is to be made to the dimensions shown. Only the angle can be varied. What…

A: Figure :

Q: the instruction is by using miscellaneous substitution. please edit the answer

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

Q: The position function of a particle is given by r(t)=At what time is the speed minimum?

A:

Q: Some airlines have restrictions on the size of items of luggage that passengers are allowed to take…

A: Let the length , width and height if the luggage is l , w and h.

Q: Find the derivative of y = x² cot-¹(3x).

A:

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: Given that: The sequence an = 3n( n + 2) .

Q: ) If g(x) = x³, then lim x-2 g(x) x - 2 - 12

A: Given query is to find statement is true or false.

Q: 2. Find f'(1) if f(x) = 3x³ (√x-2).

A:

Q: x² + y² 2-100 and 6, find . dt X dx when y 8. (Enter your answers as a comma-separated list.) dt

A:

Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s as a…

A: We can prove the convergence by using nth partial sum of the given series.

Q: Using the given graph of a curve y = f(x), determine whether each of the derivatives given below are…

A: Here we have to observe the graph.

Q: Which of the following conditions form the HYPOTHESIS for the basic form of L'Hopital's Rule? Let f…

A: Use the concept of L’Hopital’s rule when determining a limit.

Q: Find the distance from the point (-5,1,2) to the line a(t) = (-5,0, 3)t + (-7, 1, 5) -

A: According to question,Given Point : -5,1,2,Given Line : a⇀t = -5,0,-3t+-7,1,-5

Q: The volume V of the right circular cylinder of height 9 m and radius r m shown in the figure is V =…

A: