f (x) = | ef(t) + e² dx then f(x) is equal to ee -1+1 2ee-1 O 4. seçenek O 1. seçenek 2ee -1 +1 2ee -1 – 1 |

Q: y(x²-1)dx + (x³+8y-3x)dy =0  when x=0, y=1

A: Given: 3y2(x2-1)dx+(x3+8y-3x)dy=0initial condition is x=0,y=1

Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

A: The given equation is

Q: 3. If 2 = x² – x* + 6x – 5, then dty evaluated at x = 1 is dx4 dx (А) 8 (B) 36 (C) 96 (D) 120

A: To calculate the nth derivative of function y, differentiate y four times with respect to…

Q: (3 - x) dx is equal to ° S (3 − x) dx + ["' (3 + x) dx °₁ (3 - x) dx ° L₁ (3+2)dz + f (3-2) x) dx x)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: e2x-1 If y = prove that = 1- y² dx

A: Given :y=e2x-1e2x+1

Q: Find y': y = ez² + 3x² + e²e Oy = e + 3x ln x + e²ex Oy' = e + 3x²-1 Oy = e + 3x² In a Oy = e +…

A: Given y=e12x+3xe+e2e Given query is to find the derivative y'

Q: 1-x -x? dy dx -1 J-V1-x² (1 + x + y)² X.

A:

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

A:

Q: 2. (e2y – y cos xy)dx + (2xe2y - x cos xy + 2y)dy = 0

A: Exact differential equation

Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A: The Leibnitz rule for differentiation under integral sign is,…

Q: 3. fy dy + 10g = e + dt +7 -2t

A:

Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx – (3x- y – 4)dy = 0

A:

Q: 2. Find the General Solutioh oG (əx -3y-2) dx-Cx-2y) dy =0

A:

Q: y3 r³ – 4x – 1 = 0 3 Find dy/dx and explain why dy/dx is always positive. Where on the interval [0,…

A:

Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

A:

Q: Q4 Find dy for all of : dx 2- y = 3 x(x-2) x2 +1 1- y = xvInx

A:

Q: 2. Find (x) which satisfies (4e y − 1)dx + e dy = 0. O p(x) = e¯² + 5e-4x O p(x) = 3e e-4x O p(x)…

A:

Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvInx 2- у 3D x2+1

A:

Q: 2. Find by implicit differentiation. dy dx 4 (a) x +xy +y = 5 2 2 3 =D5 3 2. (b) x- xy + y 3. =D1

A: Recall: An equation of the form f(x ,y)=0 , in which y cannot be expressed directly in terms of…

Q: Sin²y dy V1 -x, given that y(-3) = 0. dx 2) Snow that the general solution for (x2 +x-6)dy = 4y dx…

A: Given that  The following differential equations

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: 4) (x- y)dx+(3x+ y)dy =0, when x = 2, y = -1 5) (3x - 2 y²) y'= 2.xy, when x = 0, y =-1

A:

Q: 1² + 3x + 4 If t = (r² – 1) what is dt/dx?

A: We have to find derivative

Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: (2xcosy + 3x2)dx + (x3 − x2siny − y)dy = 0, if f(0) = 2.

A:

Q: [2x*yžcosx² – 2x*yå + x/5]dx + [x/5stnx² - x° /9]dy = 0 3 2x²yz + x [x/ysinx? – x³ /y]dy = 0 -

A:

Q: d S[e-In(2t+1)]dr. find g(x) - dx A e-In(2x+1) 2 B (2x + 1)² (2x + 1)² (2x+1)² If g(x) = D

A: We have to find out the derivative

Q: y(x - 6y)dx - x(2x - 9y)dy = 0; when x=1, y=1 a. y?(2y-3x) = 3x2 O b. y?(2y+3x) = x² c. y2(3y-x) =…

A:

Q: dy then dx If y = In(x/x² + 1), 2x2 + 1 C) x/x² + 1 2a2 +1 D) x(x² + 1) x² + x +1 E) x(x² + 1) 1 A)…

A: Find the derivative

Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvlnx 2- у %3 V x2+1

A:

Q: d²y 1. dx² - dy - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

A:

Q: 3. Find the General and Particular solution of = 3y ; y= 3,when x = 0 dx

A: Take integration on both side and then put initial value

Q: dy Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) x2+1

A: See the details solution in below

Q: O For the bvp d²y - 9y = 3x, y(0) = y(1) = 0 the Green's functions G(x, §) satisfies d²G(x,£) -…

A: The greens function satisfies the homogeneous differential equation, not the non - homogeneous…

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: x²-x +Vx dx integralini hesaplayınız. x3

A: Please go through the attached solution. I hope that it  will help you .Thankyou . Best regards.

Q: SSS(x² + y²) dV where E lies between x² + y² +z² = 4 and x² + y² + z² = 9

A: E

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: dy If ey dx 3x2 and y (1) = 2, then the particular solution y (x) is, O y = ln(x³) + 2 O y = x³ + e²…

A:

Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

A:

Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

A:

Q: 1-S dx ; 1-e-2x y2 + 2r +

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: x(y-1) dx + (x +1) dy -0

A:

Q: 42. a. Find df /dx if f(x) = 2 In. dt. b. Find f(0).

A: Solution is given.

Q: 1-y Q2: Evaluate fo y²(x² + y²)dx dy -1

A:

Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

A:

Q: dy Find the general solution of (x² + 4). = xy. dx

A:

Q: 3y(x2 - 1)dx+(x +8y–3x)dy= 0 when x= 0, y=1 |

A: Given: 3y(x2 −1)dx+(x3 +8y−3x)dy= 0 when x= 0, y=1

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.