Write the sigma form for sin(x^2), Write the first 4 terms of the series approximation, and use the terms to create a series approximation for the antiderivitive of the function sin(x^2)

Q: Let a = ci + j and b = 6i + 36j. Find c so that a and b are orthogonal. C = i

A:

Q: Use r = 6cos(7 θ) and r = 6

A: r1 = 6                                              1r2 = 6cos7θ      θ ∈0,π…

Q: An integrating factor is μ(y) = The solution in implicit form is = c, for any constant c.

A:

Q: 2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave…

A: First derivative test: If the first derivative of the function is positive over an interval, then,…

Q: Find the limit, if it exists. lim (---)

A: Given that a limit problem and we solve this problem by using general property of limit.   Here i…

Q: * Evaluate. [12 [20x cos(5x² - 1)]dx

A: The given integral is   ∫20xcos5x2-1 dx We solve the integral using proper substitution .

Q: P(2,-3,4), Q(4,4,5), T(1,2,7) forms a triangle. find the vector projection of QP parallel on QT.

A: Proj. of QP→ on QT→ = QP→·QT→QT→WhereQP→ = Q-PQT→ = Q-T --------------------------------------------…

Q: 1. The following integration can be solved by using the Substitution f 14 dx = ♦ (Choose the correct…

A: use a different techniques to solve this problem.

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1+ 3 1. lim x12x² + x1

A:

Q: d Calculater₁(t) r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly and…

A:

Q: lim x →3 (x − 3) tan(9 — x²) sin²(2x - 6)

A:

Q: fe²x+Inx² sin x² dx = e2x cos x² dx

A:

Q: a) Find Maclaurin series generated by the following function f(x) = e-3x by Test the following…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

A:

Q: d d Calculate[r₁(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and…

A: This question can be solved using the concept of dot and cross product of two vectors and…

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 3t³i + 6tj - t²k (a) r(t) (b) r"(t) (c)…

A: Given data÷

Q: V. Given: 2. Find f'(2), if it exists. el3z-61-2, f(x)=[2x - 5], √x²-9, if x ≤2 if 2 3

A: Solution is given below:

Q: Find the solution of the given initial value problem in explicit form. Determine the interval in…

A:

Q: Write TRUE if the statement is correct, otherwise write FALSE. y y = h'(x) (-3,0) (3,0) x (-1,-2)…

A: To write TRUE if the statement is correct, otherwise to write FALSE. Suppose that hx is continuous…

Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

A:

Q: Problem 4 For x,y,z E R 5x +y Given: 2x - 2y 3x +3y and xyz = -48. Find: S = x+y+z +z = 0 +2z = 0…

A:

Q: y = tan-¹ (cosh x) (sin²x) (sech x) secz (use logarithm

A: We have to find dx/dy

Q: (x + 2)(6x - 1) (6 - x)(4x + 2) Find the horizontal asymptote of f(x) = 4- y=

A:

Q: 15x² x3-43x - 19 - (x + 1)²(x² - 6x +13) Ax + B S ax²+bx+c The integral What is the value of dx can…

A:

Q: Find the curvature and the radius of curvature at the stated point. ㅠ r(t)=10cos(t)i+11sin(t)j+9tk;…

A:

Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

A:

Q: Determine the values of r for which the given differential equation has solutions of the form y =…

A:

Q: 314! What is the value of the expression 5! ? A 3 5 B 5 C 42 D 3,991,680

A:

Q: The junior class has 50 students. Fifteen students take only French, 5 students take only Latin, and…

A:

Q: 5. (a) Find the exact value of sin (20) given that sin (0) = 3/5 and 0 is in quadrant II. (b) If cos…

A: Given problems:- 5. (a) Find the exact value of sin (2θ) given that sin (θ) = 3/5 and θ is in…

Q: 2. lim (√²-x-√x² + x)

A:

Q: -π/4 x3 dx (x²+4)5/2 (Use trigonometric substitution)

A: We have to solve above question useing trigonometry substitution

Q: ست مارت منطقه مصرف سرت

A:

Q: /² sin sin ( π/4 x² dx (x²+4)5/2 (Use trigonometric substitution) fe2x+Inx² sin x² dx = = Find f…

A:

Q: Sa 2x²+2+x³+x² =dx = [Aƒ (x) — B ln(g(x)] + D fb dx, and if A = ,B<0, then f(x) dx x+2 x² 2x + + 5…

A:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: Use differentials and the graph off to approximate the following. (Round your answers to three…

A:

Q: Find the vector component of v = 2i - j + 3k along b = 4i + 8j + 8k and the vector component of v…

A:

Q: dy II. Find Do not simplify your answers. da 1. log3 (√2x² + y) + tan(x - 7") = sin ¹1 (x²-1) +

A:

Q: 5-10 Find the area under the curve y = f(x) over the stated interval. 5. f(x) = x³; [2, 3] 7. f(x) =…

A: Area

Q: Evaluate the integral √(4 by making the appropriate substitution: u √ (432² dx [ X (4x² + 11) 7 = X…

A:

Q: Two copies of the same Rational Function are shown below. On the graph below draw the Horizontal…

A:

Q: How many different 8-digit phone numbers do not contain the digit 6? Assume that any digit in the…

A: To determine how many different 8‐digit phone numbers do not contain the digit 6. Assume that any…

Q: 13-30 Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. 4. L_ Ax 4x(1-x²)…

A:

Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

Q: 12. lim [ln(t) sin(t)] t→0+

A:

Q: A continuous O Ext F(XI = Find ***** V-V- K x has CDF X Co oxx cl 15X value of k 16 17 18 19 20 21…

A:

Q: For each of the following integrations, choose the method that can be used to find its solution.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Summary of Derivatives of Transcen Let u be a differentiable function of z du (a)(e) =eu dr (b)(b) =…

A: To express the derivative of transcendental functions.

Q: nto v. t of u orthogonal to v.

A: