Differentiate the function and express the final answer in factored form.  f(x) = (2x^3 + 7)^100(3x^2 - 8)^50

Q: II. Solve the following problems. Enclose final answer. 7.Find of z = 2x³ - 5xy² xy

A:

Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

A:

Q: perfect-square trinomial is a trinomial that is the square of a monomial. 0 صواب ( خطأ

A: Is a perfect square trinomial is a trinomial that is the square of a monomial

Q: Determine the area of the triangle bounded by the coordinate axes and the tangent to ² - y = 0 at x…

A: Let's find area (A).

Q: Which of the quantities is nearest to the value of * exp 0.003 1.001 cos (0.002) ? O 1 O 1.001 O…

A: This can be answered using calculator since the exponential and cosine value can't be find…

Q: 3. Using the Gauss-Seidel method make three iterations for the linear svstem x(0) = 0, 4x - y -z =…

A:

Q: 3. y = 1 √x Calculate y'. 1 V3

A:

Q: 4. Lim (² x-0 1 Arctanx.

A: Solution Given data  limx→0 (1x-1Arctan(x)) Find-Evaluate the Limit

Q: Prove the series diverges through Alternaeting Test. +∞ Σ (−1)α α1/2 α=1

A: Alternating series test

Q: Consider the function f(x) = x−2 (x^2−x+1)^2 Find a)  The intervals on which f is increasing. b)…

A: This is a problem related to function calculation. Based on the general formula and concept we will…

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We have to find the volume.

Q: General solution of dy dx = tan²(x + y) dx

A: This question can be solved by taking x+y=t

Q: Differentiate   f(x) = (4x3 + 1)2   using the product rule.

A:

Q: 5. Given z = arctan (), Find əz/ay

A: We can answer the question as below.

Q: 1. INTEGRALS AND ITS APPLICATIONS x2- √(¹-2)² dx S

A: Solution is here

Q: (u)n zu = (u)x

A: Given problem:- Find the Z Transform of a given signal.  x(n) = n2 u(n)

Q: Solve the following. Choose five In(x+2) dx 1. S 2x+4 2. fx² ex dx 3. f tan³x dx 12 dx 1+9x² x-2 5.…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: for a system of two equations in two variables, the graph of the equations are the same lines, then…

A: We have to find out the solution existence

Q: A. Determine whether each integral is improper. If it is improper, give your justification. 1² d 4.

A:

Q: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

A:

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A:

Q: C) Determine the area of the shaded region about the x-axis.

A:

Q: x²-3x-4 Lim x- x²-1

A: The solution is given below:

Q: O. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A:

Q: 3√3 dx X²³√x² +9

A:

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

A: Using logarithmic function

Q: The measure of the side of a square is 7 units, with a possible error of 0.02 unit. Estimate the…

A: As we know the area of the square is: A=a2 Where a is the side of the square.   Given: a=7 units,…

Q: A body temperature of 50°F is placed outdoor where the temperature is 100°F. If after 5 minutes the…

A:

Q: Lim (sinx)* -0+

A: Given query is to find the limit of the expression.

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

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

Q: 5. Find the volume of the tetrahedron bounded by the coordinate planes and the plane 3x + 6y + 4z -…

A:

Q: A lumbering battle tank's treads applied wildly varying forces in order to propel it to move…

A: We know that,  Work = force * displacement    W = F * x  = 10x(1-e-0.03x2+0.2cosx)

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A:

Q: Expand the quotient by partial fractions. x²+3 x² - 13x+42 ²+3 x²-13x+42 (Simplify your answer.)

A: Given :x2+3x2-13x+42

Q: 3.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

A: apply Pythagoras

Q: Integrate the equation using the method in trigonometric

A:

Q: (c) Evaluate 0 √3x - x² dx.

A: Given: I=∫033x-x2dx   As we know that; ∫cosax+bdx=1asinax+b+C

Q: 7. Which of the following is the differential equation satisfied by the given by the particular…

A:

Q: Numerical Integration: 5 (2x² – 3x) dx 2. 2

A:

Q: (a) Verify that tanh P-tanh Q 1-tanh P tanh ọ tanh( P – Q)

A:

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A:

Q: Solve the following problems. Enclose final answe 8x+4 (x-2)² 2 2. The Minimum point of y =

A: Topic:- application of derivatives

Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

A: From Newton’s Law of Cooling, we know that: T(t) = Ts + (To – Ts) e-kt Where, t = time, T(t) =…

Q: a cylinder is inscribed in a sphere of radius a,solve for the maximum volume.complete solution.

A: Given problem:- A cylinder is inscribed in a sphere of radius a,solve for the maximum volume

Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curve about the…

A:

Q: 15. The piecewise function -t+ + 0 st < 1 f(t) = ²+1 1st <2 -3 t22 can be expressed in terms of a…

A: This is a problem related to heaviside function which is also known as step function. Based on the…

Q: 2 = xey + yex, Find x az z дх' ду

A:

Q: 27 The x-intercept of the line x=6y +9 is (9,0) صواب ه خطأ

A:

Q: 9² P 2 -2- -N -6 -4 4 6 f (x) above, find the following limits. answer field, in text entry mode…

A: Topic:- application of calculus