Let f'(x)= = f(x) = x² tan ¹(7x)

Q: Find the equation of the tangent plane to the curve z = ² - y² at the point (5, 4,9).

A:

Q: Find the derivative of the function using the definition of derivative. g(t) = 5 √t

A:

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 3x - 2x²…

A:

Q: Find the Maclaurin series for f(x) = What is the Maclaurin series of Σ n=0 16 1+x 16 1+x -? (Type an…

A: The given function is: fx=161+x  To find the Maclaurin series for f(x).

Q: Find the gradient of the function f(x,y)=√√3x + 4y at the point (-1,3). Then sketch the gradient…

A: Given data : Find the gradient of the functionf(x, y) =  3x+4y at the point (-1, 3) then sketch the…

Q: Over the next 5 years a major electronics corporation will invest a continuous stream of…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: Differentiate. J'(u) = xu) - (2+2)(30+2)

A:

Q: Find the orthogonal trajectories of the family of curves ax² + by² = c; with a and b held Fixed.

A:

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A:

Q: time t. Find the particle's velocity and acceleration vecto

A:

Q: Question #3 - Find the relative extrema for the function f(x)=x²-3x using the second derivative test

A: Given function , f(x)=x3-3x

Q: Find the values of x for which the infinite geometric series 1+(4x-3)+(4x−3)² +... is convergent.

A: The given geometric series 1+4x-3+4x-32+...... We have to find the values of x for which the…

Q: Complete the following problems, Please show all your work and make sure you have answered all the…

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

Q: (a) Find the inverse function of f(x) = 7x - 6. f-¹(x) = (b) The graphs of f and fare symmetric with…

A:

Q: Differentiate. h'(w) = h(w) = (w5+6w*) (w¯4 - w¯6) W X

A:

Q: 02 θυου (u? In(3u + 4v)) 3u? + 8uv (3u + 4v)a 12u? + 32uv (3u + 4v)a 12u2 – 32uv (3u + 4v)a –12u2 +…

A:

Q: What's the derivative of  y=4 sec x csc

A:

Q: The value of k so that (y³ +kxy¹ −2x)dx + (3xy² + 20x²y³)dy = 0 is an exact equation is: a. 10 b. 5…

A:

Q: Which of the following is an ordinary, linear differential equation of order 2? +k²xt = 0 d²x +k²x =…

A: Find which equation is linear differential equation of order 2.

Q: Let f and g be differentiable functions for which the following information is known: f(2)= 1, g(2)…

A:

Q: Use integration to find a general solution of the differential equation. dy do =x√-x-2

A: dydx=x-x-2dy=x-x-2dx∫(a.b)d=a∫bdx-∫((dadx)∫bdx)dx∫xndx=xn+1n+1+c

Q: Calculate the first four terms of the sequence, starting with n = 1. Cn = (-1)²n+5 C1 = C2 = C3 = C4…

A:

Q: 2. Find the points of contact of the two tangents to the curve, 6y=2x³+9x³-12x+2, parallel to the…

A:

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. (-5)"…

A:

Q: A quadratic function has its vertex at the point (3,-9). The function passes through the point…

A: The given function is: fx=ax-h2+k   Given: vertexh,k=3,-9Px,y=-2,-1

Q: Can you please use these in the solution instead x=u+h y=v+k dx=du dy=dv   Then assume: let…

A:

Q: 26. ƒ(x) = x³ + x¯³

A:

Q: Find the Taylor series generated by fat x = a. f(x) = 2 Choose the correct answer for the Taylor…

A: Use Taylor series

Q: Find an equation for the tangent plane to the surface z + 2 = xy³ cos(z) at the point (2, 1, 0)

A: I have solved step by step in detail......go through the solution

Q: Question #2 - Find the relative extrema for the function f(x)=x²-3x² using the first derivative…

A:

Q: On the basis of data obtained from a preliminary report by a geological survey team, it is estimated…

A: Given that,the rate of oil production, rt=3.935t3.45e-1.351t   thousand barrels per year.where t is…

Q: Find the Taylor series generated by fat x = a. f(x) = 3*, a = 1

A:

Q: Let h(t) Then h' (t) is h' (3) is 2+3.2 = h'' (t) is and h'' (3) is 6t-3.2

A: Let ht=2t3.2-6t-3.2.Then find  h't,h'3,h''t and h''3.

Q: Find an equation of the tangent line to the curve at the given point. 1 + sin(x) cos(x) (π, -1)…

A: Given: y=1+sin(x)cos(x), (π, -1)

Q: An orthonormal basis for 2 -(9 V = span 0 is given by... 1 0 -2/3 1/3] 1/2] 2/3 -1/2 1/2 1/3] 2/3 0…

A:

Q: Step 4 Now we have the following. √₁ xy² ds = √2/²2² + ds = x/2 (5 cos(t))(5 sin(t)) 4(5 dt) *π/2…

A:

Q: B. lim f(x) = x-0+ D. f(0) = F. lim f(x) = x→2+ H. f(2)=

A: Given query is to find indicated limits from the graph.

Q: How long will it take $5000 to grow to $7500 at a simple rate interest rate of 8% ?

A:

Q: Let f'(x) = ƒ(x) = (8x² − 8)^(2x² — 6) ¹²

A:

Q: The cost of producing xx units of stuffed alligator toys is c(x)=0.002x^2+6x+5000. Find the marginal…

A:

Q: Find the length of the curve x = 3 + 1 from y = 1 to y = 2.

A:

Q: Question 3 Which of the following is an antiderivative of f(x) = cos (x²-5) ? sin (x5 – 5) A B © sin…

A: To find the antiderivative of the given function.

Q: . Solve the IVP: 2x²ydy − 1 = x¹, y(1) = 1. You must give your solution in explicit form.

A: 2x2ydydx-1=x4y(1)=12x2ydydx=x4+1∫xndx=xn+1n+1+c

Q: Write the first five terms of the sequence: [11 Inn n a₁ = Determine whether the sequence converges,…

A: To find the first five terms of the given sequence and to determine whether it diverges or not.

Q: The graph of the equation x2/3 + y2/3 = 102/3 is one of a family of curves called astroids because…

A:

Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

A: (a)  x5+81(x2-x)(x4+18x2+81)we know  (x2-x)=x(x-1)(x4+18x2+81)=(x2+9)2

Q: Suppose that lim an = 4 and lim bn = 9. n→∞ n→∞

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Find the equation of the specified line. y(x) = through (1, 9) parallel to x - 9y = 9

A:

Q: 80. Skydiving A skydiver in free fall subject to gravitational acceleration and air resistance has a…

A:

Q: Use symbolic notation and fractions where needed. Enter DNE if the series diverges.) 7.(-3)" 11" =2

A: Given query is to find the sum of the series.