8 i) 이름을 . dx ii) f xel+x2 dx

Q: Find the distance between the point P(1, 1, 1) and the surface x² + 2y² + 3x² = 1.

A: Given Point P1, 1, 1 and surface x2+2y2+3z2=1

Q: ) .  Consider a minimal threshold value for a species to survive, T. One way to add in this factor…

A: answer is in next step.

Q: An even function f(x) for all values of x and x holds a. f(x) = f(-x) b. f(x) = -f(x) c. f(x) =…

A:

Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

A:

Q: Minder with a closed top and bottom is to have a volume of 101 cubic inches. If the cost of the…

A:

Q: Find the exact sum of the following series O. In 3 2 1 In(3) --- / 2 In ( ²2 ) 32 3 In (²2) - ○…

A:

Q: Find the nth term of a sequence whose first several terms are given. 3, 5, 3, 5, 3, 5, ... an =

A:

Q: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the…

A: The general equation of function of temperature is given by÷ D=asin[bt-c]+d Now we need all the…

Q: At which of the marked values of x is A. f(x) greatest? x = B. f(x) least? x = c. f'(x) greatest? x…

A: Note:- According to company guideline we can do maximum 3 sub parts so i am solving here first 3

Q: Our goal is to approximate the positive real number x that satisfies sin(x) = x³. We will apply…

A: Our goal is to approximate the positive real number x that satisfies sinx=x3We will apply Newton's…

Q: to the graph above, which of the following statements is correct: x) changes sign from + to - x) > 0…

A: Topic:- calculus

Q: Euler found the sum of the p-series with p = 4: 3(4) - Σ Σ n = 1 Use Euler's result to find the sum…

A:

Q: 11. A rubber ball is dropped from a height of 5 feet and bounces to 1/3 of its height after each…

A:

Q: 15. 1/√/2 X 1+ 4x4 dx

A: We need to evaluate :

Q: The original question did not put it right. it was (5overx) 5/x If  f(x) = 3x + 4 and g(x) =5/x

A:

Q: 5 4 3 2 -2 2 The graph above shows the base of an object. Compute the value of the volume of the…

A: Given Cross section perpendicular to the base is square.

Q: Consider the following. (Round your answers to four decimal places.) f(x, y) = x cos(y) (a) Find…

A:

Q: Problem #3: Consider the following statements. (1) Σ n=0 (-1)" 2n+1 X² (2n + 1)! = X- ∞ (iii) The…

A:

Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

A:

Q: 2,0 Va Find the formula for f. f(x) = 0

A:

Q: Use implicit differentiation in finding y'. 1. x² + y² =18xy 2. x²y + xy² = 6

A: Given,x3+y3=18xyDifferentiate w.r.t.'x'(Use product…

Q: Find all cube roots of the complex number −1 + i

A: We have to find all the cube roots of the given complex number.

Q: For the following equations, enter y if the equation defines y as a function of x but not vice…

A: y if the equation defines y as a function of z but not vice versa, x if the equation defines z as a…

Q: Find the critical value(s) of f(x) = 7√x – x², to two decimal places as needed. Separate multiple…

A:

Q: n Use the comparison test to determine if the series n=1n²³+²+1 converges or diverges.

A: The given series is ∑n=1∞nn3+n+1 we have to find the series is converges or diverges, by using…

Q: 7. Prove: cos(0 + 2) 7) = sine.

A:

Q: Rewrite the following as a sum of trigonometric functions with no powers greater than 1. cos² (2x) =…

A:

Q: Using De Moivre's formula demonstrate that sin(3x) = 3sinx − 4sin3x

A: Given that sin3x=3sinx-4sin^3x De moivres formula is (cos x+ i * sin x) ^ n = cos n*x+ i * sin n*x -…

Q: Determine the explicit formula for the n-th term of the sequence written below. Note that the first…

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

Q: It is a fact that the function  f(x) =  (9x2 − 2) (4x2 + 4)  has a limiting value. Use a table of…

A: We need to find limiting value.

Q: Suppose that f(x) = 2x4 + 9x2. Evaluate each of the following: f'(1) = f'(-3) =

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 1. Find the volume generated by revolving about x=1, the area bounded by y = (x²-₁)² and the x-axis.…

A: We have to find the volume generated by the given function.

Q: If f(t) = 2 - 9t cos t find f'(0).

A: Given :ft=2-9tcost

Q: Four functions are given below. Perform the indicated compositions to determine which functions are…

A:

Q: Problem 10. Find the inflection points of f(x) = 8x + 110x³ - 42x² + 10. (Give your answers as a…

A:

Q: Problem 12. Find the absolute maximum and absolute minimum values of the function over each of the…

A:

Q: Use Stokes's Theorem to evaluate F. dr. Use a computer algebra system to verify your results. In…

A: Here,  g(x,y)=49-x2G(x,y,z)=z-g(x,y)

Q: Use the Laplace transform to solve the following initial value problem: y" - 6y +9y=0 y(0) = 5, y(0)…

A:

Q: Let f(x) = Then f'(x) = m = b = 3 sin x 6 sin x + 2 cos x The equation of the tangent line to y =…

A:

Q: Let f be the function defined by f(x) = sin 2x + cos 7x and let g be the function defined by g(u) =…

A:

Q: Evaluate f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

A:

Q: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

A:

Q: Using the Limit Comparison Test with the geometric series -17, to 8 67 determine if the series given…

A: Limit comparison test -  If we have two series ∑n=1∞an and ∑n=1∞ bn and limn→∞(an/bn) is finite and…

Q: In *In ecot³x dx feln sinx

A: We need to evaluate integral.

Q: Our goal is to approximate the positive real number x that satisfies sin(x) = x³. We will apply…

A: Given, f(x)=x3-sin(x)

Q: 4. The height h in centimeters of Shuntaro's pogo stick from the ground as he jumps on it since s…

A: We have to find the height at given times.

Q: Use the Laplace transform to solve the following initial value problem: y" +9y= cos(6t) y(0) = 0,…

A: given y''+9y=cos(6t) taking laplace on both sides  L{ y''+9y}=L{cos(6t)} L{y''}+L{9y}=L{cos(6t)}…

Q: 3. KIN 2 13² cos x V1+sin x dx

A: The given integral, ∫0π2cos x1+sinxdx

Q: Evaluate f2Tof 1 0 rdrde

A: The given integral is: I=∫02π∫01rdrdθ   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: 3. 4. T 2 S² 0 π COS X /1 + sin x dx s sinx + 2 cos x dx

A: The objective is to find the integral.