gaokao 2019 Q7

gaokao · China · national-III-arts Tangents, normals and gradients Determine unknown parameters from tangent conditions

7. The tangent line to the curve $y = a \mathrm { e } ^ { x } + x \ln x$ at the point $( 1 , a e )$ has equation $y = 2 x + b$ . Then
A. $a = \mathrm { e } , b = - 1$
B. $a = \mathrm { e } , b = 1$
C. $a = \mathrm { e } ^ { - 1 } , b = 1$
D. $a = \mathrm { e } ^ { - 1 } , b = - 1$

Given non-zero vectors $\boldsymbol { a } , \boldsymbol { b }$ satisfying $| \boldsymbol { a } | = 2 | \boldsymbol { b } |$, and $( \boldsymbol { a } - \boldsymbol { b } ) \perp$

7. The tangent line to the curve $y = a \mathrm { e } ^ { x } + x \ln x$ at the point $( 1 , a e )$ has equation $y = 2 x + b$ . Then\\
A. $a = \mathrm { e } , b = - 1$\\
B. $a = \mathrm { e } , b = 1$\\
C. $a = \mathrm { e } ^ { - 1 } , b = 1$\\
D. $a = \mathrm { e } ^ { - 1 } , b = - 1$

Paper Questions

Q1 Q2 Q3 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19