J₁ f(x, y) = 4x + 7y and D = {(x, y)|0 ≤ x ≤ 1, x³ ≤ y ≤ x³ + 1} Evaluate the double integral f(x, y) dA over the region D.

Q: 4. Determine the value(s) of x when the functions y = same slope. (1 + x) and y = 2x° have tangents…

A: Topic = Application of derivative

Q: 215. y = 6u³, u = 7x - 4

A: Topic = Derivative

Q: Differentiate the following function.   f(x)=2e^3x   D/dx(2e^3x)=

A: f(x)=2e3x

Q: 3² Find the equation of the tangent line to the curve (an ellipse) + = 1 at the point (-2,√108). The…

A:

Q: Which of the following is a convergent p-series? (A Β Σ m=1 (D © Σ C Σ(3) n=1 η n=1 n Σ(4) 3

A:

Q: 2. Calculate 5(1+2x³) dx by using: S (a) Calculate in term of n the sum = f(x) 4x to approximate the…

A: Given : ∫051+2x3dx a) Let I = ∫051+2x3dx fx=1+2x3, h=5-0n=5n, a=0, b=5

Q: Solve the equation. Give an exact answer using the log function and an approximate solution to 4…

A:

Q: 3. Show that there are no tangents to the curve f(x) = 9x³ + 2x² that are parallel to the line 2y +…

A:

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

A: Given Data : Here we have given two curves y=x and y=x2 form x=0 to x=1.   Required : We have to…

Q: (d) f(x) = log3 (6x − 1) - ln(6x - 1) + 4eª − e¹x - 1 a logb

A:

Q: Find the centroid (x, y) of the region bounded by π π and y 0. : = y = 7 cos(3x), x 6' X - 6'

A:

Q: A college student works in both the school cafeteria and library. She works no more than 12 hours…

A: Given that student works no more than 12 hours per week at cafeteria and 16 hours per week at the…

Q: 6. Find the each of the following limits using rules of limits. a. x²+x-6 lim x→2 x-2 b. lim √x² - 9…

A: Limits

Q: Find the derivative. y = 9x-2 - 5x3 - OA. dy 중증 중증 중증 중증 dx OB. dy dx O C. dy dx O D. dy dx 5x° +…

A:

Q: (g) = In(){ f(In(1)sin (3x) dx In (x) = x 4 cos (3) (1">)in (~ = In (x) (1 sin" (2 X (h) f(x) =…

A:

Q: Let f(x)=3e^x+4+e^−4 f′(0)=

A:

Q: V4UE Test: Unit 1 Rates of Change An object is dropped from a height of s meters and it takes it t…

A:

Q: the demand function q = D(p) = 459 – p, find the following. For a) The elasticity b) The elasticity…

A:

Q: Determine the global extreme values of the function f(x, y) = x³ + x²y +9y² on x, y ≥ 0, x + y ≤ 2.

A:

Q: Given y = (u² + 1), u = x² = 5, determine when x = dx - 2.

A:

Q: If h(2) = 6 and h'(2) = −2, find d (h(x) dx X :). x = 2

A: Topic = Derivative

Q: alculate the average  rate of change of the given function over the given interval. Where…

A: Given: x 0 1 2 3 f(x) -5 8 3 1 Interval [0,2]

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by…

A:

Q: Find the centroid of the region bounded by the given curves. y = 6 sin 2x, y = 6 cos 2x, x = 0, (x,…

A:

Q: Write the scalar equation of each line given the normal vector ñ and point P a) = [11, -5], Po(4, 9)…

A: Note:- Since you asked multiple sub parts questions ,as per our policy we can solve first three sub…

Q: Find the point(s) on the graph of f where the tangent line is horizontal. f(x) = X x² + 25

A:

Q: Find the derivative of the function. g(x) = (1 + 5x)5(5 + x − x²)8 g'(x) = || X

A: To find the derivative of the following function. gx=1+5x55+x-x28

Q: (2n-1)! n! (c) [d) { cos(x)} n

A: If the limit at infinity of the sequence exist then sequnce is convergent.

Q: n { ( ₁ + ² )"} n (f) {n(√n² +1− n)} (e)

A: Sequence is convergent if limit of the sequence exists finitely.

Q: Integrate TT y 2 x² dy dx.

A: To integrate ∫13∫24yx2 dy dx.

Q: Find an equation of the tangent line to the curve at the given point. y = (1 + 5x)¹2, (0, 1)

A: To Find : Equation of tangent line to the curve y=(1+5x)12     at point (0,1)

Q: increasing decreasing g(x) = x4 - 18x² + 5

A:

Q: Solve for x. log₂ (x − 28) = 3 X = (Separate answers by a comma.) If the answer is radical use…

A:

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞…

A:

Q: 3) Find Domain and Range of the function; 1 2x-5 f(x) =

A:

Q: A transport company manages a fleet of 60 trucks of three different models. The elderly carry a…

A:

Q: Calculate the Taylor polynomials T₂ and T3 centered at x = a for the function f(x) = 11 ln (x + 1),…

A:

Q: Recall that the volume of a sphere is given by V = ²³. The radius of a spherical balloon is…

A: Given that Volume of sphere is V=43πr3and drdt=3cm/min , r=12 cmwe have to dVdt

Q: Solve and write interval notation for the solution set. Then graph the solution set. -2<2x+1<7…

A:

Q: Find the derivative of the function. f(0) = cos(0²)

A: To find the derivative of given function

Q: Let f(x) = −3x² + 1 1 X3 + −xª. Find all local and absolute maxima and minima of f.

A:

Q: 2. 3 Determine f'(x) and simplify. f(x) = (3x² - 4x) (2x - 3) ³

A: Topic = Derivative

Q: A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: hypotenuse

A:

Q: Let f(x) =x√x² + 1. Sketch a graph of f. Make sure your graph takes into account regions of f…

A:

Q: et f(x) = xe. Find where f is increasing and decreasing, and concave up and concave down.

A:

Q: 3. Let A = a. b. 1-2 3 1 1 1 Find the Null space of A. Find a basis for Null space of A. c. Find the…

A:

Q: Solve the following for x. Give an exact answer using the log function. 7. (94-6) = 77 X =

A:

Q: O Take a standard 8.5 in. by 11 in. page of paper. You're going to cut square corners of equal size…

A: According to question,We have,Dimension of paper : 8.5 in. × 11 in.

Q: 37 4 4. Find the first four nonzero terms of the power series for f(x) = sinx centered at x = .

A: Please see the below picture for detailed solution.