The exponent in the exponential form is the value of the logarithm. (A) True B) False

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

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Q: IV. INDETERMINATE FORMS Show if the following limits produce an indeterminate form. Then, evaluate…

A: The objective is to evaluate the limit.

Q: (a) The total surface area of an open cylinder is 27 cm³ given that radius, rcm. i. Show that the…

A: Given that; Total surface area of am open cylinder is 27pi cm^3. Radius r cm.

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

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

Q: O O O O It is reflected over the x-axis and shifted right three units. It is reflected over the…

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Q: x²-3x-4 Lim x- x²-1

A: The solution is given below:

Q: 1 Lim x-0* x 1 sin x

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Q: Which of the following methods can be applied to find a particular solution yp of y" +y = cos(ex)?…

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Q: Lim x²-4 x-x-6

A: Using L-Hospitals rule

Q: Using the method of undetermined coefficients, the modified form of a particular solution for the…

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Q: 5. The auxiliary equation of the differential equation (4D³ - 13D + 6)y = 0 falls under Prove your…

A: Given; ( 4D^3-13D+6)y=0

Q: Ifv= (x² + y² +2²)−¹, then 320 + + is 8²v 8² Əy² 822 1 -1 -1/2 Other:

A: Given that     v = (x2+y2+z2)-1/2

Q: Given the domain 9 = {(1, y) | − 4 ≤ x ≤ 4, - 4 ≤ y ≤ 4}:: D the double integral of f(x, y) = 1 over…

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Q: Find the measures of the angles of the triangle whose vertices are A=(-2,0), B=(3,3), and C=(1,-1).…

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Q: 7. Find the area between f(x)=-x² + 4x and g(x) = x² - 6x +5 over the interval 0≤x≤1 Ei..

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Q: The length of a rectangle is given by 4t - 3 and its height is √21, where t is time in seconds and…

A: We know that area of a rectangle is defined as (length of rectangle)(Height of the rectangle)

Q: Prove 3. The auxiliary equation of the differential equation (D² - 6D+9)y = 0 falls under. your…

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Q: For a period of time, an island's population grows at a rate proportional to its population. If the…

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Q: Using the method of variation of parameters, the form of a particular solution pof (D²+25)y=4x²-3e5x…

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Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

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Q: [ * ² {( x=-62² ) + x ² (2 X-67 ° S - XP(x - 5] [9_xP ( _ex-b^) -b). E [+5₁ dx=6₂ 3 My = 3dx = 1/2/2

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Q: Let L(z) be the linearization of f(x) = sin x + 1 at the point x = . Find L(1/2). O -1 pi/2-1…

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Q: The function is x % = y? What is 8 2 dude Y æ2

A: We need to find derivative.

Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

A: The given curves are; y=4x and y=x-32 So, the bounded region is as shown below. Apply the disk…

Q: 8. The general solution of y"- y = x²ex + 5

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

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Q: 4. Use the washer method to determine the volume of the solid obtained by the revolving the region…

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Q: z = xey + yex, Find əz əz дх'ду

A: Given: z=xey+yex To find : ∂z∂x,∂z∂y For ∂z∂x, we have to do the partial differentiation of z with…

Q: Question 3 Iff is continuous on [a,b], then T True F False b then f(x)dx = f(x)dx T a

A: Here it is given that f is continuous on [a,b] From the integration we can take the constant value…

Q: 02/Use the l'Hopital's rule to find the limits in t3-4t+15 a) lim t--3 t²-t-12 X-8x² X-00 12x²+5x b)…

A: Given problem:-

Q: 1. Newton's Law of Cooling: At 9:00PM., a thermometer reading 70°F is taken outdoors where the…

A: Note: Unit of temperature °FTs1=Outdoor temp or surorunding temp 1          = 15°FTo=Thermometer…

Q: Q1/ Find the area of the region bounded by the given curve (y=x²-5) and the curve (x = = -) by means…

A: Given y=x^2-5 & x=-y/4

Q: 15. The piecewise function -t+ 0 ≤ 2 can be expressed in terms of a Heaviside function as:

A: We are given a piecewise function  f(t) =-t       0≤t<1t2+1      1≤t<2-3               2≤t…

Q: must

A: When a curve changes from concave down to concave up or concave up to concave down , that means…

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s. How fast does the tip of…

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Q: 1. Evaluate the following limits (a) (b) x sin r lim 2-0 1- cos x lim (1+a/x), a, b>0 x →+∞

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Q: 3/ find the area for the region in the first quadrant bounded by the curve (y = 4x - x²) and line (y…

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Q: 10. The current to a projection lamp is measured at 4.7 A when the line voltage is 115.45 V. find…

A: 10)  P=VI P=115.45*4.7 P=542.615 watt(w)

Q: Find the values of p for which each integral converges. 2 80 dx dx b. x(In x)P x(In x)P GELEH 2 dx…

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Q: Numerical Integration: r2 1 S² = = X 0 1. dx

A: Please find the solution:-

Q: a. Find the critical numbers of f on the given interval b. Determine the absolute extreme values of…

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Q: What is the value of C if r(π/3)=2? * O 2 0 TT/2 none of the choices

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Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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Q: y'+xy=xy^3 Solve for the solution What is the integrating factor? What is the dependent variable?

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Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the disk method to determine the volume of solid obtained by…

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Q: Find L(e³t cos 2t)

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Q: = 4 R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

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Q: Find ?хду of z = x3 + 5x² y + 6

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Q: Find the surface area when C {(x, y): 0 ≤ x ≤ 2; y = 1 is revolved about the y-axis.

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Q: (Differential Equations) A thermometer is taken from an inside room to the outside, where the air…

A: It is given that A thermometer is taken from an inside room to the outside, where the air…