7) Relative to an origin O, the position vectors of the points A and B are given by OA P (-) and OB= +- (²+²) 4 -2 Find a) the value of the constant p for which the angle BOA = 90⁰ b) the unit vector in the direction of AB when p = 2 c) the position vector of the foot of the perpendicular from point A to the line which passes through O and B in the case where p = -1.

Q: Find the indefinite integral. Solution in handwritten a. S sin x -dx cos²x

A:

Q: n of Calculus to find the derivative of the

A:

Q: 1. (a) f(x) = cos x ln x Find the derivatives of each of the following functions. (b) f(x) =…

A: Given :f(x)=cosx lnxf(x)=ln(cosx)

Q: What two nonnegative real numbers with a sum of 66 have the largest possible product? The numbers…

A:

Q: x²+2x+1 dx (x+2)(x−1)²

A:

Q: (1 + x³) dy - x² y dx || 0

A:

Q: Use the formula к(t): k(t) ||r' (t) x r"(t)|| 3 ||r' (t)||³ r(t) = esti + e¯tj = to find (t). #1

A:

Q: Evaluate the following integrals by substitution. Show your complete solution. Express your answer…

A: We have to find integral solution

Q: 4. Find the volume of the solid that lies under the paraboloid z = x? + y² and above the region R in…

A: We want to find the volume.

Q: Find the exact length of the polar curve. r = e4?,    0 ≤ ? ≤ 2?

A:

Q: Let f(x)=√18 x. Compute f'(2) using the limit definition f'(2) = Find an equation of the tangent…

A:

Q: +² = x² dx

A: We have to solve the given differential equation

Q: Let f(x) = 25 x The slope of the tangent line to the graph of f(x) at the point (–6, – 25) is The…

A: All the answers are given below

Q: 109. f(x)=x* tan x³ -x In (1+x2), then the value of (b) 1 dª f(x) dx 4 at x = 0, is: (d) 15

A:

Q: nd the maximum profit and the number of units that must be produced and sold in order to yield the…

A: Given the query is to find the maximum profit.

Q: Figure (a) shows a vacant lot with an 80 ft frontage in a development. To estimate its area, we…

A: It is midpoint Riemann sum      here length of interval  △x=20

Q: 304² 3x Evaluate dx dy, by first Reversing the order of integrals. √36 + x3 Enter an integer or a…

A:

Q: A farmer wants to construct a fence around an area of 6936 square feet in a rectangular field and…

A:

Q: Determine the position function if the acceleration function is a(t) = 6sin t+5, the initial…

A:

Q: Find the first four terms of the binomial series for the given function. (1+5x)1/2 5 125 25 OA. 1-x+…

A: We can find the first four terms as below.

Q: 5. By the Fundamental Theorem of Calculus (Newton-Leibnitz Theorem) √² + x² d VX evaluate

A:

Q: Use the method Laplace transform to solve the following. (a) 2r' + 7r=3e-t, x(0) = 4. (b) 2r' +…

A:

Q: 7. Use Lagrange Multiplier to find the maximum and minimum values of the function f(x, y) = x²y…

A:

Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = , y =…

A:

Q: 3. Find an equation for the parabola with directrix at r = 3 and focus (-1,-1). Find the two latus…

A:

Q: The fadius of a right Circular cylinder is increasing at a rate of 2 units Per Second. The height of…

A: Rate

Q: Show the repeating decimal .2727272727 repeating.... as an infinite geometric series. Give sum of…

A: This question can be solved using the concept of infinite geometric series.

Q: Ⓒ'Evaluate Sot So Sox sing ²sin y dy dz dx tim of the

A:

Q: Find the arc length L of the graph of r(t). r(t) = 9 cos(t)i +9 sin(t)j + tk, 0≤t≤ 2π

A: This is a problem of vectors and integration. Based on concepts and formula of arc length we will…

Q: Find the indefinite integral. a. fsecy (tany - sec y )dy b. f(x²-9)(2x)dx

A:

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A:

Q: 2.Figure out the following = 2t2 +Int, t>0 dy. = cos(t – 1) c.f(z) =| -1|,9(z) =| 1.f'(1)?g/(0)? ?…

A:

Q: Use the appropriate technique of integration to compute the following antiderivatives. SHOW THE…

A: Solve the following

Q: ZzJm 3. Use integral test to determine whether the series 4. Use an appropriate test to determine…

A: 3. ∑n=1∞e-n2n4. ∑n=1∞n2n+1!n! 22n

Q: Consider the vectors. (5, -8), (-4,1) (a) Find the dot product of the two vectors. -28 (b) Find the…

A: Given problem:- Consider the vectors.   <5, -8>, <-4,1>   (a) Find the dot product of…

Q: Find the indefinite integral. Solution in handwritten. 1. f(-8x)√3-4x²dx

A:

Q: 2000, the population of a city was 71,000. The population had grown to 100,000 by 2011. If the…

A: Given query is to find the population in 2026.

Q: The Haycock formula for approximating the surface area S, in square meters (m²), of a human is given…

A:

Q: x² + 4xy + y² = 13, (2, 1)

A:

Q: Given the following acceleration function of an object moving along a line, find the position…

A:

Q: c. f(-8x)√√3-4x² dx d. S dx 6x² (4x³-9)3

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 8 1 = lim t+x6t²+7'2t (?, ?)

A: Explanation of the answer is as follows

Q: Question 7  A business spends $80,000 on Marketing, $100,000 on R&D,  and $ 12,000 on Expenses.…

A: We have to find the ratio between spending.

Q: ∞ n=1 (n+1)(3² − 1)¹ 32n

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Height is given by f(t)f(t)=-16t2+420t+6t =11.5

Q: Suppose that sec(t) = 3/2 and that tis in quadrant IV. Find the exact value of tan(t). -3/2 -$5 O -…

A: 1 +tan2(t) = sec2(t) In Quadrant 4th , secant and cosine are positive. Note : As per our Guidelines…

Q: Find the volume of the solid that results when the region bounded by y = x and y = x², from x = 0 to…

A:

Q: Find the Taylor series generated by fat x = a. 1 f(x)=, a=9

A:

Q: Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find…

A: