4-f(t)=e-²¹.t³.

Q: a) Find the outward flux of the vector field F(x, y, z) = x³i+y³j + (z³ + xz)k across the surface of…

A: Concept: Divergence theorem: According to the Divergence theorem, the Surface Integral of the Normal…

Q: APPLICATIONS OF DERIVATIVES PROBLEM: An 80 cm piece of wire is cut into two pieces. One piece is…

A: TOPIC = APPLICATIONS OF DERIVATIVES

Q: Simplify the expression from the previous step by canceling the common factors. sin ²0+ The…

A:

Q: Find the volume of the figure. Round to the arest tenth if necessary 12 in 13 in.

A: Given query is to find the volume of the figure.

Q: Q3: Evaluate the following integrate: (chose three only) 1. dx 1+x²

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

Q: 34. Compute the surface area generated when the first quadrant portion of the curve x² - 4y + 8 = 0…

A:

Q: 8. f sec² (3x - 1) dx

A:

Q: f(x) = -3 sin x [0, 3T]

A:

Q: 26. Find the equation of the tangent line to the curve h(x) = √3x − 1 at x = 3 3 A. y − 2 = ³/(x +…

A: 26.   The curve h(x)=3x-1 at x=53 Note:      Multiple questions are given, we are answer only one…

Q: Vector is a real number (positive or negative). O True O False

A: To Check: Vector is a real number or not.

Q: 38. The polar equation of the curve is expressed as r = 2sin 0 + 2cose. Compute the perimeter of the…

A: I am attaching image so that you understand each and every step.

Q: (3) dx x 1+√x

A:

Q: -4 dx 2. 510

A:

Q: Find y'. x3 +yở = 8£y

A:

Q: 13. Find the area bounded by the curve y=- y=2 and a lower limit of y=10. A. 1.61 C. 1.81 B. 2.61 D.…

A: Area

Q: Prove the following using the definition of a limit. n - 1 (a) lim n+on+1 (b) lim (2x² − 3) = −3 -…

A: For (a),    limn→∞ n-1n+1=limn→∞ 1-1n1+1n=limn→∞ 1-1nlimn→∞ 1+1n=11=1 For (b),    limx→ 02x2-3Plug…

Q: A) Consider the function f(x) whose second derivative is f"(x)=4x+3sin(x). If f(0)=4 and f'(0)=4,…

A:

Q: 5. A tank is full of water. Find the work required to pump the water out of the spout. Water weighs…

A: A tank is full of water. Find the work required to pump the water out of the spout .water weight is…

Q: Find the solution of e*tyy' = 3x given y(1) = 3.

A:

Q: which method is best to describe an infinite set?

A: The solution is given below

Q: 2. The mode score on the 6th grade math test was 94. Which of these interpretations must be correct?…

A:

Q: Given f’(x)= 3 cos x - 9 sin x and f(0)= -6 find f(x)

A: We can solve this as follows:

Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

Q: If; of t = x then at t=1 is (Note that these functions in N) dx

A:

Q: 6. f 2x³sin (3x) dx

A:

Q: Solve the following problem by the two-phase method: Maximize -₁ - 2x2 subject to 3x₁ + 4x₂ ≤ 12 X1…

A: We need to maximize the value.

Q: In reference to the following function: f(x) = x^2 + 7x + 13 / x + 4 What is f’(x)?

A: Given problem:- f(x) = x2 + 7x + 13/x + 4 Find:-f’(x)?

Q: The gradient of the function 2x1 + x2 − 3 evaluated in x = (0 0 0)² is: OA. Vf= (1 2 3)T OB. Vf=(0 0…

A: ∇f =i∂∂x+j∂∂y+k∂∂zf

Q: Express Ln(z) in the form a + b. (Simplify your answer completely.)

A:

Q: Use the graph of h(x) shown below to evaluate lim_h(x), if possible. If the limit does not exist,…

A:

Q: write the equation y=a(x-1)^2-9 in intercept form

A: The given equation,   y=ax-12-9

Q: a) Y= ezx-e-zx €²x+e-2x

A: Given,   y=e2x-e-2xe2x+e-2x

Q: 3. (x²+x+4) dx

A:

Q: The number of people living in Canada rose by 1.2% to 38.5 million in 2021. If this population…

A:

Q: and p(n) iF IF Fon) = 4 sec t dz.

A:

Q: 5. Find the surface area of the figure. ************ 20m 5 20m

A:

Q: 11+22=

A: Topic = Algebra 11+22=33

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the functi h(x) = = 60%…

A: We have to find derivative

Q: Express In(z) in the form a + ib. (Simplify your z = -ei In(z) n = 0, 11, 12,..

A: Given complex number  z=-ei

Q: Find the slope of the secant line between x = 3 and x = 4 for the function f(x) = −x² − 2x + 4.…

A:

Q: 30. Find the surface area generated when the portion of the curve y² = 12x from x = 0, x = 3 is…

A:

Q: If a loading ramp is placed next to a truck, at a height of 8 feet, and the ramp is 22 feet long,…

A: If a loading ramp is place next to truck, at a height of 8 feet and the ramp is 22 feet long To…

Q: Find the surface area of the hemisphere: 6 cr

A: Given that hemisphere and the redius of this hemisphere is 6 cm. We find surface area of this…

Q: Which of the following conic sections could be formed when a plane intersects a cone at a shallow,…

A:

Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power series…

A: Given the expression,∑n=2∞nn-1cnxn-2+∑n=0∞cnxn+2

Q: Kiara invested her savings into a Registered Retirement Savings Plan (RRSP) at an interest rate of…

A: This question can be solved using the concept of compound interest.

Q: Determine the domain and range of the function. 2+ 1 1-3 1-2

A:

Q: Express In(z) in the form a + ib. (Simplify your answer completely.) z = -5 + 5/ In(z) = n = 0, ±1,…

A:

Q: Solve the following limits by algebraic method and by the corresponding theorems b) lim (senx)m x-0…

A: use the trigonometric identity to solve the limit.

Q: Sketch the region that corresponds to the given inequalities. 5x  −  y  ≥  0 x  −  2y ≤ 0 x ≥  0, y…

A: