- The equation of the sphere centered at C(h, k, l) and radius r is given by (x − h)² + (y − k)² + (z − 1)² = p² Find the center and radius of the sphere with equation x² + y² + x² - 4x + 2y + 6z · - 11 = 0 (HINT: Use completing the squares) -

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A:

Q: Let f(x) be defined by Find f'(1). f(x) = (2x - 1).

A:

Q: The given family of functions is the general solution of the differential equation on the indicated…

A:

Q: Solve the following inequality. (x+5)(x+3)(x-7) <0

A:

Q: find X so that the net present worth of the investment is zero

A: answer is given in step2

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: We need to find y2.

Q: Find curl(F x G) = V x (F x G). F(x, y, z)= i + 7xj + 6yk G(x, y, z) = xi - yj + zk

A:

Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

A: We want to find the area of region bounded between the given curves

Q: Find a particular solution to Ур = y" + 7y + 10y = 15te¹.

A:

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. - 1/2 (u = v), y = 1/2 (u…

A: Jacobian ∂(x,y)/∂(u,v)= ∂x/∂u* ∂y/∂v - ∂y/∂u* ∂x/∂v

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy

A:

Q: A vector with magnitude 9 points in a direction 160 degrees counterclockwise from the positive x…

A:

Q: Find the (a) derivative y'= dy dx y = (n² + 5 secx) ㅠ of following Question tog 3 x

A: Note: Due to guidelines i can solve only your first question. Solution: a) y=πe+5sec xlog3x…

Q: Evaluate I= I=S 2+41 Iti NJ Z 2 dz

A: This question is related to definite integration, we will solve it using given information.

Q: 6. Evaluate the following real integrals by residue theorem 3 • I- 88 151 +47 O dx (x²+1)(x² +9) ans…

A:

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

A:

Q: The given family of functions is the general solution of the differential equation on the indicated…

A:

Q: Is using the Quotient Rule equivalent to using the L'Hospital's Rule? Explain. Please use clear…

A: We have to explain, using the Quotient Rule equivalent to using the L'Hospital's Rule.

Q: Question 18 -6 -5 -4 -3 -2 -1 8+ (2) 7 65 4 32 My 1 -1 -2 -3 --4- ✓ to t 1 3 Find an equation for…

A:

Q: Find the following integrals. Do not add any constants of integration, as the resulting functions…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1 3. How many terms of the convergent p-series k=1² must be summed to obtain an approximation that…

A: We have to find no. of terms of the convergent p series.

Q: Exercise (c) Use the results of part (b) to estimate the slope of the tangent line to the graph of…

A: Given.

Q: A tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is…

A: Basic differential equation is used

Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find the slope of the tangent line to the curve y = f(x)…

A:

Q: Find the derivative of f(x) = = 30 6/4x+1 Enclose numerators and denominators in parentheses. For…

A:

Q: Consider the equation below. 12 3-sin (8) (a) Find the eccentricity. e " (b) Identify the conic. O…

A: Given equation :- r=123-sin(θ)

Q: Evaluate the limit. 1-x² lim *+1 sin(27x) a) lim b) x+2x² C) lim - - 2x *→(π/2)- (2-) tan r Show all…

A:

Q: Suppose that the position (a) Find the velocity at tin v(t) = 17 S (b) Find the velocity at tin

A: topic:- application  of derivatives

Q: Q5 100 5+2³+ [In(In r)] lim a) 1+ 7 +6² + [In(In x)]200 cos x ln(x-7) *-+*+ In (e-e) b) lim

A:

Q: the artery, Artery = distance of dv dt x mm per sec per yr R ne blood from the center of the artery,…

A: topic:- application of derivatives

Q: A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of…

A: A  force 540 Newton stretches 3 meters .a mass of 45 kg  is atteched to the end of the spring and is…

Q: Express the number –2 in the form R(cos(0) + i sin(0)) = Re where R> 0 and 0 ≤ 0 ≤ 2π. NOTE: Enter…

A:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 進 ↑ -6+ <||||||||||| Hex

A:

Q: need

A:

Q: Differentiate y = sec a tan . y' -

A:

Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

A:

Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: Find the dimensions (in inches) of the open-top cylindrical tin can with volume 125 cubic inches…

A:

Q: The Taylor series for True False 1 at x = 3 is 1-(x-3) + (x − 3)² − (x − 3)³ + ... X-2

A: Topic = Series TRUE

Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface x² – 2y² − 3 ² = −4…

A:

Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

A: Find the volume of the solid bounded by the curve Z=ln(x2+y2)z=0x2+y2≥1x2+y2≤9

Q: 21

A:

Q: d) Consider f(t) = bt, where t&R and b ER such that 0 by [Select] e) 5 log25 k² = k where k denotes…

A: To label the following statements as T for true or F for false.d Consider ft=bt, where t∈R and b∈R…

Q: Question 17 V -2 8- 7 16 16 6 5- 4 3 رها را 2 1 -4 -7 1 > V V 2 3 4 5 Find an equation for the graph…

A:

Q: Use the Factor Theorem to determine whether x+3 is a factor of P(x) = 2x³ + 6x²-x-4 Specifically,…

A:

Q: 8 -6 4 수 +

A:

Q: Let - fot² Find the average value of f on the interval [0, 1]. f(x) = dt.

A:

Q: Find the general solution of the given higher-order differential equation. y"" - 2y" - 3y' = 0 y(x)…

A:

Q: Graph the following function, showing all asymptotes and relative extreme points. 16 O TV.W.N f(x) =…

A:

Q: Find the Jacobian (x, y) / d(u, v) for the indicated change of variables. x=u-v², y = u + v a(x, y)…

A: Follow the procedure given below.