A spherical balloon is inflating with helium at a rate of 128x ft / min. How fast is the balloon's radius increasing at the instant the radius is 4 ft? How fast is the surface area increasing? The balloon's radius is increasing at a rate of ft / min at the instant the radius is 4 ft. (Simplify your answer.) The surface area is increasing at a rate of ft/ min at the instant the radius is 4 ft. (Type an exact answer, using t as needed.)

Q: QUESTION 4 Suppose that x2 -v3 +2xy= 12. Use implicit differentiation as presented in Section 14.5 t...

A:

Q: Q2) if the vechrs V=-i +5 and ū=Tz i+5J+2 R Find a) The scalev component of ū in the divection of V ...

A:

Q: Find the equation of the tangent line to the curve y 2x cos x at the point (п, — 2т). The equation o...

A: We will find the equation of tangent line. 

Q: If f(t) = 7t3 – 10t2 + 8t – 4, find f'(t) and f"(t). f'(t) = f"(t) =

A:

Q: u? + 5u – 7 If g(u) In(u) find g'(u)

A: The given function,    g(u)=u2+5u-7ln(u)

Q: Problem 3.1 Prove that if x is a positive real number, then LV[]] = [V]

A:

Q: COla-sina COIa- da sin (2a)

A:

Q: figure. What should be the dimensions of each enclosure if the total area is to be a maximum? What i...

A:

Q: Hw Fin ow and dw for the fallowing functions e 2- X+リ

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: A rancher has 300 feet of fencing to enclose two adjacent rectangular corrals, as shown in the follo...

A: A rancher has 300 feet of fencing to enclose two adjacent rectangular corrals, the equation describi...

Q: Determine whether the series converges. 1 k=1 Vk + 11

A: This question is related to the series convergence or divergence.

Q: Use Green's Function to assist in solve the following initial-value problem. (Section 4.8) y" – y' =...

A: Given:    y '' - y' =1              ,        y(0) = 10    , y' (0)  =1

Q: Зах + b Find the derivative of h(x) Assume a, b and c are | 5c constants. h'(x) = %3D

A: The objective is to find the derivative. 

Q: Find a point c satisfying the Mean Value Theorem for y=sqrtx on the interval [9,25]

A:

Q: Given f(x) 7 find f'(x) using the limit definition of the derivative. f' (x)=

A:

Q: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate...

A:

Q: Determine whether the seauence converges or diverges. If it conveges, find the R lo0?+nl00+(nn) 00 n...

A:

Q: A metal sheet is situated in the xy plane so that the temperature T = T(x, y), in degrees Celsius, a...

A:

Q: What is the coefficient of the term contaning the variable h when f(x +h) – f(x) is performed, and i...

A: Here we have to determine the coefficient of the term containing the variable h when f(x+h)-f(x)h is...

Q: Find the derivative of g(u) = square root of ((u+1)/(3u+2))

A:

Q: EX g. Evalnab..f.x.d. wha. R.ia. the.regizn.in.the frirg t.. quadrant..bounded..Xy=16. Soluedidy

A:

Q: Consider the function on the interval (0, 2x). f(z) = 5 + cos(x) (a) Find the open intervals on whic...

A: Here, the given function is: f(x)=π2+cos (x)⇒f'(x)=-sin x

Q: Find the equation of the tangent line to the function f(x)=2x^2-x at the point where x=-1. Give you...

A:

Q: Consider the function f(x)=x^5 - 5x^4 a. Find where the function is increasing and decreasing.   ...

A: Increasing and Decreasing functions : If f'(x)>0 for every x on some interval ,then f(x) is incr...

Q: cot dv 3. cot (v²+9) 1-cos² - Iem

A:

Q: 7.4 Q7.4 Find the taylor series for fcx) = centered at a= 2 (-1)**1 (1 + 1) 00 (A) Σ (x- 2y (B) E (-...

A:

Q: Vove erf C-∞)= -I or J edt=-1 STT

A:

Q: 7 Let f(x) = 7 The slope of the tangent line to the graph of f(x) at the point - 3, is The equation ...

A:

Q: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per y...

A: Given population of world in 2015  was 9.75 billionlet   for t=0 , we have year 2015

Q: 4. p² –1) cos[cosh (In r)]dr let u= du=

A:

Q: Find the Taylor series for f(x) =- centered at a = 2.

A:

Q: Use the Comparison Theorem to de x + 1 36 dx Ji O convergent O divergent 8

A:

Q: *csch(2 sin 2x)cx 1. V1-4x let u= du=

A:

Q: 5. Which of the following functions is NOT continuous everywhere? A. f(x)= mx + c, where m, c eR x² ...

A:

Q: 8. a. Using the vectors = (3, 3, 1) and ỷ = (-1, 2, –3), verify that the following formula is true: ...

A:

Q: 2. -4

A: Our Aim is to evaluate the integral given below:-∫dyyy8-4 -(i)

Q: Try to observe the graphs below : y f(x): y= f(x) y3f(x) y = f(x) (a) (b) (c) (d)

A:

Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all tha...

A: f(x)= (x-2)(x-5)(x-7) , [2,7] 

Q: Find the area of the surface generated by revolving the curve - 5x y = e x > 0

A:

Q: Let f(x) = /71 – x The slope of the tangent line to the graph of f(x) at the point (7, 8) is The equ...

A:

Q: Verify that the given point is on the curve and find the lines that are (a) tangent and (b) normal t...

A: Given that Curve y2-3x-9y+12=0 point -2,3Solution:put point on the curve  y2-3x-9y+12=0 32-3-2-9×3+1...

Q: 11 10 81 7- 4 3 + -1 0 1 2 3 4 5 6 7 6

A:

Q: cate whether lim f (x) and f(c) are equal or unequal at th ate whether lim f (x) or f(c) does not ex...

A: In this question we will use basic concepts of calculus i.e concept of limits. Solution of the above...

Q: 2y (x+2)² dy dx'x² – 4 x – 4

A:

Q: 5. r(t) = (t°/3) i + (12/2) j, t>0 %3D 6. r(t) = (cos³ t) i + (sin³t) j, 0<t< a/2 %3D

A: This question is about finding vectors   k, b &amp; t   

Q: 2+7 sin cos z zp-

A: Given: ∫2+7sin3zcos2zdz

Q: Consider the function f(x)= x^2−3x.   Compute the derivative using the definition

A: In order to solve this question we will use the concept of first principle which defines derivative.

Q: Solve using horizantal S,ļide EX g. Evaluabt.fx.d. wha..ia.the..rsgem.in.the first quadrant.bounded....

A:

Q: Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider...

A:

Q: Evaluate O y°dx – x°dy, where C is the boundary of the region between the circles a? + y? = 9 and x?...

A: To evaluate the integral.