Vectors: given vectors Add/subtract/scalar multiplication: Length/Magnitude: u =( - 3,- 1,4) and v =( - 2,3,2) Dot product: Find 2u- v Is u more than 20% shorter than v? Find u v

Q: Find the distance from the point P(1, 2, −1) to the line passing through the points A(−2, −3, −5)…

A:

Q: 26. What is the value of lim A. - 2 B. - 1 1-cost t→0 t C.0 D. 1 - ?

A:

Q: 22. Suppose that lim f(x) = x, what is the value of lim 5. (f(x))² ? x-3 A. 41 C. 45 B. 43 D. 47 23.…

A:

Q: . Expand the binomial (2x - 1)*.

A: Binomial theorem

Q: y = (1+x)² 2 x² 2

A:

Q: z = xey + y ex

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

Q: Let P be the point with Cartesian coordinates (6, 9), and C be the plane curve with parametric…

A:

Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² -z = 0…

A:

Q: Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

A:

Q: Solve for the Partial Derivatives and total differential of each of the following function

A:

Q: Find the equation of the tangent line to the curve y = 5x² - 7 at a point x = 1.

A:

Q: -0.45|-2.8x - 4.06| 2.5

A: Here we have -0.45-2.8x-4.06-2.5

Q: 4 The slope of the tangent line to the curve y = X at the point 5, is: 5

A:

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 4y - y² and y =…

A:

Q: 3. Find the average value of the function on the given interval. a. f (x) = 4x − x², [0,3] 2 2 b. f…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: ds Find the complete solution of = 8t³ √s. dt

A:

Q: 16. Evaluate the integral or show that it is divergent dx x+1 1 (a) √ (3x+1)³², I (3+1), (b) /…

A: We need to find out here  integrals.

Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: We have to find the volume.

Q: dy Find the complete solution of 2e-2 cosx- dx Note: fedu=e" + C - sin² x = 0.

A:

Q: Determine whether each of the ff.differential equation is separable or not,if it is…

A:

Q: 3 N -3 -2 -1 1 2 3 1 . For the above function f(x) = 2 1.2, estimate f'(x) using h = 0.001 for the…

A:

Q: Find the exact maximum and minimum volumes (in cm) of a rectangular box whose surface area is 1,300…

A:

Q: given below. t lim f(x) = -8, lim g(x) = 5, and lim h(x) = 4 X-C X-C X-C 17. Find lim[f(x) = g(x)]…

A:

Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

Q: Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1)…

A:

Q: Find the Area of the Surface obtained by rotating the curve about the y y = √√x, 1 ≤ y ≤2

A:

Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² + 5, the x-axis and…

A: Given: y=x2+5 Graph of the functions given are

Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: 5. Suppose f is continuous on [2, 8]. Use the table of values of f to f(x) dx using a left, right,…

A:

Q: ector equation of the line that...... gh (3,9) and (-7,1) b) is perpendicular to the line 5x-3y-8= 0…

A: We will solve the problem

Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A:

Q: 1. Evaluate the integrals (a) fxsin 2xdx, (b) f(3x - 1) eª dx, Hint: Use the Integration by Parts. 3…

A: SOLUTION-

Q: The area bounded by the parabola ay=x², the x-axis, and the line x=b is revolved about the y-axis.…

A:

Q: [* [b3 - 3 3 dy

A:

Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

A: Solution :Without odd-even…

Q: 1. Write the polar form of the following complex number Z = 3

A: We know that polar form of complex number z=x+iy is z=r(cosθ+isinθ) Where r=x2+y2θ=tan-1(yx)

Q: the particular solution

A:

Q: x-5 X-3+x-3' 31. Determine the lim A. 0 B. -00 C. +∞ D. does not exist

A:

Q: T/6 3 coss 3x dx

A:

Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t = - dt

A: Given that the differential equation  ds/dt=10*csc^2(2t) Determine by s=2 when t=pai/4  To find the…

Q: Ex: If w cos(uv), u = = xyz, y = π 4(x²+y²)' aw find at point (1, 1, 1). əx

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change o ƒ(x) = 5x² +…

A: We have to find rate of change

Q: Provide all answers to four (4) decimal places. Applying the Gauss-Seidel method in solving the…

A:

Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

A:

Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

A:

Q: _ ²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8 Given x =

A:

Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1) b) has…

A: vector equation of line

Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A: