Find the equation(s) of a line that is tangent to f(x) =4x - x² and pass through P (2,5). (Provide detailed solution) Oy = 2(x+2)-5 y=2(x-2)+5 Oy 12 (x-2) + 5 O None of the choices y = ±2 (x+2)-5

Q: e integral be 'solvable' using trigonometric substitution. What is the correct choice of u given J…

A:

Q: The reverse order of fo Say હરે e² dxdy is equal to e-1 8e None of them

A:

Q: In (x-2) lim x2+ In (x² −4)

A:

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: The improper integral A 0 B 1 с e D 8 +∞ St 0 ex dx is

A:

Q: I sin sin ³0cos Ode by trigonometric transformation, we use the identity; To evaluate the integral…

A: We have to slove integral

Q: Evaluate: L{cos(3+2t)} s cos32sin3 A s²+4

A:

Q: efv. Evaluate dx Use rationalizing substitution. A B 8 √e² - 2 - 2√2 Arctan — √e² - 2 + C e³ − 2 −…

A: Let's evaluate given integral by using rationalizing substitution.

Q: Solve the integral: S- ® in/1+x A) an 1 B_5n/1+x' 5 6 1 √√√x + x + C + C c dx

A:

Q: 2.2 5 (2x² – 3x) dx

A: We have to evaluate

Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

A:

Q: A solution of a differential equation free from arbitrary constants obtained from the general…

A: The complete Solution of an Ordinary differential equation is composed of a general solution and a…

Q: We can apply General Power Formula of Integration on which of the following integrals? A / fes…

A:

Q: Evaluate: L-¹{. S-2 (s+ 2)² - 49 4 Â) e-2t(cosh7t - -sinh 7t) 4 B e²t(cosh7t + sinh 7t) (C) e2t…

A:

Q: 4 The reverse order of So Say 0 J4y +2 ex² dxdy is equal to e-1 se O None of them O

A: To evaluate the given integral by reversing  the order of the integration.∫01∫4y4ex2 dx dy

Q: Find the area bounded by : f (x)=e*, g(x)=e* and x=3. A (e²-1)² e2 sq. units B (e³+ 1)² e3 sq. units…

A:

Q: y=Arccos (x²)

A: The objective of the question is evaluate the second derivative of the given function.

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: dx x² - 4x + 13 X

A: Given  ∫dxx2-4x+13To find integral:

Q: Find Ə2z ?хду of z = x3 + 5x² y + 6

A: The objective of the question is evaluate the partial derivative .

Q: 9. What is the general solution for the differential equation y"" - 3y' - 2y = 3x? A. y C₁x +…

A:

Q: What are the dimensions of the rectangular field of maximum area that can be fenced with exactly 500…

A: First make the equation of area in terms of breath or length then diffrenciate for maximum area .

Q: dx Transforming secx + 1 2-2z² A 1+z² ® √ ₁ + 2²/1d² +z² B -dz 1-z² z²+z C / 1-z² Ⓒ / 1-²/²0 D 1+z²…

A: To find the transformation of the integral ∫dxsec x+1 after using miscellaneous substitution.

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

A:

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: 3. Look at the figure below. Find the value of x and the measure of each angle. n 1.x = 2.42 = 3.26…

A: We know that alternative interior angles are same Therefore 5x-14=3x+18 Subtract 3x+18 from both…

Q: Find the critical points of the function f(x) = x³ + ¹/5x² + 50x + 7. Use the First Derivative Test…

A: We have to find the maximum and minimum.

Q: The expanded form of the differential operator D(xD-1) is A XD²+1 B XD² C XD²-1 (D) XD²-D

A:

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: To find the work done.  Option D is correct.

Q: Suppose that f(x, y) = ²/" on the domain D = {(x, y) |0 ≤ y ≤ 1,0 ≤ x ≤y³}. D Then the double…

A: Given: fx,y=exy and D=x,y| 0≤y≤1, 0≤x≤y3   As we know the basic integration formula.…

Q: 10 Σ (3n – 1): 125 n=1 10 Σ–1 (3) -1, 125 Σ (3n – 4): 125 10 Ο Σ(3n – 4): 125 Ο Ο O e Θ

A: Verify all the option   then find the sum.

Q: Given; √ √ tex dx 2 Applying rationalizing substitution, find dx in terms (A) z dz 2+z² 2 z dz B…

A: Given query is to find the dx in terms of dz.

Q: Write TRUE or FALSE before each statement. Solve y' - ³y = dependent variable. differential…

A:

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A:

Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: me general solution of (D²-2D+1)y=2sin > A y=c1eX +C,xe* + sinx+cos x y=C1eX +C,Xe* + sinx ©…

A:

Q: C) (-∞,1]

A:

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A:

Q: . The implicit solution for the differential equation y' = x³y is A. In x = y² + c B. 3 lnx = y² + c…

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. Ⓒ unit² B unit² Ⓒunit² 2 Ⓒ unit²

A:

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

A: Please find the solution:-

Q: Find the average value of the function f(x, y) = xy over the triangle with vertices (0, 0), (1,0)…

A:

Q: √√³F(x) Which of the following can be determined given Arx (f(x) + g(x) +h(x)) dx B g(x) dx ©…

A:

Q: Evaluate: dx (x+1) log(x+1)

A:

Q: Əz 5. Givenz = y -4x ?х 6. Find of z = In(xy) a²z 7.Find of z= x³ + 5x²y + 6 əxəy Find дz

A:

Q: The general solution of (D³-5D²-6D)y=0 is Ay=c₁+c₂е¯x + c3e6x By=c₁ex+c₂e²x + c3e³x Ⓒy=c₁+c₂e²x +…

A:

Q: Evaluate the improper integral A) diverges 3 B 4 с N|9 2 3 -dx

A:

Q: tank has pure water flowing into It at 10 L/ min. The contents of the tank are kept thoroughly…

A:

Q: y = 3Arcsin (2x³) -- Arccos(2x³)

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. unit² B unit² Ⓒunt² D unit²

A: