Q1. Find the equation of sphere whose center is at (4,-1, 7) and radius is 5.

Q: 4. Suppose the function is defined by y = f(x) = x² – x a. Find the average rate of change of y with…

A:

Q: A= 4 B=5 30 - 2 Find the 5 Only) following (chease A+ B (2) 3A -B A 2B (inverse) (leng th or…

A: Solving

Q: a) obtained by rotating the curve Sketch and find the area of the surface y =/2x + 3 for x E [2,4].…

A:

Q: 5. a. Write in your own words a definition of a complex numbers and Modulus of the complex number.…

A: This question can be solved by applying the concepts of complex numbers.

Q: Which one is the sum of the geometric series 1 00 n= O 2 O 3 | 2 O Divergent 3/4

A: The sum of an infinite geometric series is given by, Sn=∑n=0∞arn=a1-r if r<1 a is the first term…

Q: Given the power series 2 (-1)" x" n = 0 Find the Integral of the Power Series. 00 A 2 (-1)" x" | dx…

A:

Q: A. Using the definition of derivative, find the derivative of the follow function. 1) f(x) = ! 2)…

A:

Q: The series 5 n 6. n=4 8

A:

Q: fm üli f (x,y,z)=x'+x*y *z ' + yz ?

A:

Q: The area of the surface generated by revolving the curve y = y9 - x2,-2 < x < 2 about the x-axis is…

A:

Q: Find an equation of the Hyperbola that has Foci (-1,–3) & (-1, 7) with asymptotes y = x+ & y = -a+…

A: Standerd equation of hyperboal is (x-h)2a2-(y-k)2b2=1where (h,k ) be the center

Q: The average value of the function y = 10 x In(4 x) on the interval [3,7] is О 50.05 O 152.14 O…

A:

Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. y =…

A:

Q: 5th derivative of y = log x^5 to the base 2

A:

Q: Given z1 = 2 - 3i, z2 = 1 - i, z3 = 3 + i; find the following a) z1 ÷ z2 ; b) Z2 Zı ; c) z1? ; d) z2…

A:

Q: a)Find the average of the function f(x)= x² +1 on the interval [-1,2] Answer:

A:

Q: Find the average value of the function LX TEX f (x) =4sin| on the interval [3,6]. COS 4

A: Dear learner, as per our guidelines we can provide the solution for first one only. Kindly post…

Q: A company invests $19,000 to produce a product that will sell for $56.85. Each unit costs $9.20 to…

A:

Q: Find an equation of the plane tangent to the following surface at the given point. V3 cos (xyz) =…

A:

Q: (x+1)(x-7) (x - 1)(x + 7) Substitute the expression for y = on the right slde of the equaton and…

A: I am attaching image so that you understand each and every step. Note:- I suggest that this type of…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. |…

A:

Q: Find the extremum of f(x,y) = 3x2y2 +2y2 + 2x2.

A:

Q: Find the limit. 300 lim er

A: limx→∞ x300ex

Q: Determine the convergence or divergence of the series. (If you need to use o or -00, enter INFINITY…

A: Given: Now,             limn→∞ 8n-13n+1=limn→∞ 8-1n3+1n=limn→∞ 8-1nlimn→∞ 3+1n=83 So, the series is…

Q: Find the net area and the area of the region bounded by y= 11 cos x and the x-axis between x= -: and…

A: Area A = ∫ f(x)dx here limit from -π/2 to π A = ∫-π/2π cosxdx A = [sinx]-π/2π  A = sinπ - sin(-π/2)…

Q: 5 s2+ 3 s2 –8

A: Let's find.

Q: Find the marginal cost for producing x units. (The cost is measured in dollars.) C = 300(6 + 5   x)…

A: We have to find the marginal cost

Q: Prove that (R x Q) N (Q × R) = Q x Q

A: This question can be solved using the concept of cartesian product of two sets and using the…

Q: Question 3 Algebraically compute f'(1) using the definition of the derivative, given that f (x) = x2…

A:

Q: Q2. Find the second order partial derivative of F(x.y) = x³+ x°y°- 2y² w.r.t. x at (2,1).

A: Given:        Fx,y=x3+x2y3-2y2  taking first partial derivative with respect to x.…

Q: Find the values of a and b such that f is differentiable at r = 3 and then sketch the graph of f if

A:

Q: Water flows into an empty reservoir at a rate of 2200 + 15t gal/hour . What is the quantity of water…

A:

Q: Find the generals solution to the following 2nd order Non Homogeneous ODE: x?y" -3xy" +4y=2x?

A:

Q: Consider the surface defined by the equation z2 = 2x² + 4x - 6y? - 2y+ 1. %3D Find a set of…

A:

Q: Determine whether the series is convergent or divergent. 1 1 + 4 + + ... 9. 16 25 Divergent…

A: 1) The given series is 1+1/4 +1/9 +1/16+ 1/25 +.....

Q: Compute the first partial derivatives of the following function. f(x.y) = 5 - tan (x?+2y?) 5=ロ

A:

Q: A company introduces a new product for which the number of units sold S is given by the equation…

A:

Q: If vector T = (x+ y+1)i+ j– (x +y)k then T.curl(T )is

A: We are given vector T.

Q: 10 Below is the graph of y = f(x). Find | f(x)dx. Round your answer to three decimal places. 5 10

A: Given:      ∫210fx dx   = Area under the curve between x=2 and x=10

Q: -angent lihe at 2 8. What is the slope (round your answer to one decimal place)? m = What is the…

A: Given, f(x) = 3.3 x2 - 7.2 x

Q: Find the exact length of the polar curve. = 02, 0s0 < T/2

A:

Q: x2 - 6 Calculate the derivative function of g(x) Write your result as a single fraction. 2x + 1 =…

A: Given: g(x)=x2-62x+1

Q: Section 1.5 In Exercises 1 and 2, we refer to a function f, but we do not provide its formula.…

A:

Q: hction given as J(E) that IS a Simplify the expression f(x + h). f(r + h) = f(r + h) – f(x) Simplify…

A: Given : f(x)=-2x+1.

Q: Given the power series 2 (-1)" x" n = 0 Find the Derivative of the Power Series. x (n + 1) d A 2…

A:

Q: Find a power series representation for f(x) = x2 1+ x3 ° By differentiating the power series…

A:

Q: Let R=[a,b]×[c,d]. || e*sinyda = e*dx S siny R. C Select one: O True False

A: This is a problem related to double integration. Based on the general formula and concept we will…

Q: Use the chain rule to find the derivative of 4(6æ° – 2")" You do not need to expand out or multiply…

A:

Q: Think of four random integers q, r, s, and t selected from 0 through 9. Let a1 = 0.qrst, where q, r,…

A: let as consider four integers q,r,s,t from 0 to 9 then we get a1=0.qrst=0 now if we select four more…

Q: Evaluate the volume of the solid generated by revolving the plane region about an axis. Show the…

A: