Use implicit differentiation to find dy dx 4xy + y2 = 3x + y dy dx

Q: Find the vectors T, N, and B at the given point. r(t) =   8 cos(t), 8 sin(t), 8 ln(cos(t))  ,…

A: The given vector is:r(t)=8 cos(t), 8 sin(t), 8 ln(cos t)and the given point is:  (8, 0, 0)Therefore…

Q: Use Taylor's Inequality to determine the number of terms of the Maclaurin series for ex that should…

A: Given Maclaurin series for ex that should be used to estimate e0.1 to within 0.0001.Taylor…

Q: Evaluate the integral. [² (8t³ i- (8t³ i − 15t² j + 15t4 k) d dt 0

A:

Q: On graph (A) draw a function that is continuous on [-2, 2]. On graph (B) draw a function that has an…

A:

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: (a)   slope =dydxy=5x2+5,  point  (-5,130)dxndx=nxn-1

Q: (a) f(x)=2x+3x²-36x (b) f(x)=x+√l-x (1) Find the intervals on which f(x) is increasing or decreas…

A: first derivative 2nd derivative

Q: Consider the following function. f(x) = sin(x),    a = pi/6,    n = 4,    0 ≤ x ≤ pi/3     (a)…

A:

Q: 5x (d) . x²-x-6 dx

A:

Q: 1 Find the slope of the crowe at given point P and an equation of the tangent line at P. y = 4-x²³,…

A: standard form of equation is y=mx+c,  where m is slope given point is  (-1,5)given  y=4-x3we know…

Q: A(x) = -0.015x³ +1.05x gives the alcohol level in an average person's bloodstream x hours after…

A:

Q: 15. For the following power series, a) find the series’ radius, R, and its interval of convergence.…

A: root test

Q: What is 1 da x√9x² - 9

A: Given,            ∫dxx9x2-9

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 6x F(x) = cos(t¹) dt. […

A: To use the fundamental theorem and find derivative

Q: find the orthogonal 2 2 x² + 3y² = C trajectory of the family OF Curves

A:

Q: Determine the area bounded by y = x² - 2x + 1 and y = 7 - x.

A: Given: y=x2-2x+1y=7-x

Q: 1. Evaluate the following geometric series, (find its sum) or show that it diverges. a) Σ=0" cos(nn)…

A: Sum of series

Q: The cost C'(x), where is the number of miles driven, of renting a car for a day is $48 plus $0.95…

A: Let's find linear function.

Q: Suppose F(4) = 6, F(6) = − 4, and F'(x) = f(x). 6 L² (2x²4 + 4 (x² + 4ƒ(x) + 10) dx

A:

Q: means the derivative of the inverse function, evaluated at b. O U O b 1 (ƒ-¹)' (b) a f'(a) 1 ƒ' (ƒ-¹…

A: To determine the derivative of inverse function

Q: 3) (i) The velocity and acceleration of a particle is given as v=-4i -9j + 5k and a= 6i- j + 3k Find…

A:

Q: Find the radius of convergence R of the series. 2" (x + 5)^ √n R = Σ n=1 I = H|N 1 2 Find the…

A:

Q: Given the function g(n) = √6n+1, solve g(n) = 3 for n. Provide your answer below: n =

A: given  g(n)=6n+1  and g(n)=3there for  6n+1=3

Q: Use the relation lim 0-0 lim t→0 sin kt t A. lim t-0 sin 0 0 = 1 to determine the limit. (k…

A:

Q: EXAMPLE 7 Sketch the conic below and find its foci. 25x²9y²-150x + 36y + 414 = 0 SOLUTION We…

A:

Q: Use double integral to find the area of the region bounded by the one leaf of the rose r = a cos 20.…

A:

Q: Frequency 10+ 8 6 1 7 13 19 25 31 37 data Based on the histogram above, what is the class width?…

A:

Q: Find the an equation of the hyperbola satisfying the given conditions. Foci at (-13,0) and (13,0);…

A:

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: To find the equation of tangent to the given curve.

Q: Which rule is faster to use to differentiate f (2)=(22) (*) ? Use the Product Rule O Simplify to 3…

A:

Q: Consider the functions y = (x - 2)² +3. 13. a. Find the inverse of the function. b. Find f-¹(-4). If…

A:

Q: Solve 6 sin(26)- 1 cos(p) = 0 for all solutions 0 < < 2π Φ Give your answers accurate to at least 2…

A: NOTE: Refresh your page if you can't see any equations. . for simplicity take,  use the formula

Q: A ball is being inflated such that the volume is increasing at a constant rate of 130cm3/s. How fast…

A: Given query is to find rate of change of radius.

Q: Consider the given function and the given interval. 22x f(x) = [0, 2] (1+x²)² (a) Find the average…

A: Given, fx=22x1+x22, 0,2 Formulas used, The average value of a function f(x) in the interval [a, b]…

Q: Evaluate the following integral. 3 400 F 2 - 20x dx

A: We are required to find ∫400x3-20x2dx

Q: Shown below is the region R bounded by the coordinate axes, the parabola y² = 2x – 2, and the…

A:

Q: part 1) following transformations: S a) £¯¹ { (s+ 3)² +9 L b) L{(t+1) e-2t+e³tcos (5t))} = c) C) 2-1…

A: To find transformation. As per our guidelines we are supposed to answer?️ only one question. Kindly…

Q: Find the following limits. Show your work. x² + 3x lim a) x-4 x² - x - 12 lim b) x-0 tan(x) X

A:

Q: The graph of a function f(x) is given: 6 5 4 3 2 -2 -1 di 7 7 1 2 3 4 5 6 7

A: Concept ∫abf( x )dx = area under the curve from a to b

Q: Volume generated by x² = 4y, y = 0, x = 4 and rotated with respect to the y axis.

A:

Q: Given f(1) = 4, f'(1) = 7, if g(x) = 4x(f(x) - 2)² then g'(1) =

A:

Q: The polynomial f(x) given below has -2 as a zero. f(x) = x³ + 12x² +54x +68 Find the other zeros of…

A:

Q: Question 3: Supply the missing constant, k, so that the resulting trinomial is a perfect square.…

A: The given polynomial is:x2-8x+p

Q: 2. Suppose that f(x) = ((.x² + x·5).5 +.r.5).5 when x ≥ 0. Find df(x)/dx. •5 (@ï¥2³ )² +x²)+…

A: The answer is given in step 2

Q: 13) Consider the graph of f' below. How many total local extrema (maxima or minima) does f(x) have?…

A: Graph of the derivative function f' is given. We have to find the number of local extremum of f.

Q: Given - 3x² dy dx B) Find the slope of the tangent line drawn to the graph of − 3x² − 2xy + 3y³ = 25…

A:

Q: 2 1 पीपीप -2 -4 The curve above is the graph of a sinusoidal function. It goes through the points…

A:

Q: O O Let F(s) = O est 5 e5t 5 est 5 + 6|5 t 5 O 6e5t 5 None of the others 1 s²-5 s 1 5 then £¹{F(s)}…

A:

Q: 1) If f is decreasing on (a,b) then f'(x) b. 15) If e* >0 then k>0 and x>0. 16) f(x)=e is an…

A:

Q: List all of the proper factors of 70. (Enter your answers as a comma-separated list.)

A: Proper factors of a number include all its factor except itself.

Q: Explain why the following is NOT continuous at x=3. What type of discontinuity is it? USE A LIMIT…

A: